# Difference between revisions of "Scrambler"

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Score is calculated by the following formula: | Score is calculated by the following formula: | ||

− | + | :Score = 3 x (running time in seconds)+(stopping distance in cm) | |

Lowest score wins. The best running time of the two runs is used. Generally the stopping distance is measured perpendicularly to the wall, to the nearest millimeter. However, depending on the location of the competition sometimes measurement to the nearest decimeter can be used. | Lowest score wins. The best running time of the two runs is used. Generally the stopping distance is measured perpendicularly to the wall, to the nearest millimeter. However, depending on the location of the competition sometimes measurement to the nearest decimeter can be used. | ||

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The wheels mass, or more appropriately, its rotational inertia is one of the important of those properties. As we know from physics, the resistance to acceleration in a linear motion is different from the resistance to acceleration in a rotational motion. It is notable that the wheel in a scrambler is a rolling object, and thus it is a great mistake to ignore both components of its motion. It is a well known derivation from physics that the total energy of the rolling wheel is: | The wheels mass, or more appropriately, its rotational inertia is one of the important of those properties. As we know from physics, the resistance to acceleration in a linear motion is different from the resistance to acceleration in a rotational motion. It is notable that the wheel in a scrambler is a rolling object, and thus it is a great mistake to ignore both components of its motion. It is a well known derivation from physics that the total energy of the rolling wheel is: | ||

− | + | <ol start="1"> | |

+ | <li><math>E = 1/2 (m R^2 + I) \times omega^2</math></li> | ||

+ | </ol> | ||

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Note that radial velocity is easily related to the normal velocity of the wheel(and thus the car it is attached to by a simple equation: | Note that radial velocity is easily related to the normal velocity of the wheel(and thus the car it is attached to by a simple equation: | ||

− | + | <ol start="2"> | |

+ | <li><math>v = omega \times R</math></li> | ||

+ | </ol> | ||

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− | + | <ol start="3"> | |

+ | <li><math>F_f = m g k</math></li> | ||

+ | </ol> | ||

− | '' | + | ''F<sub>f</sub> |

− | + | <ol start="4"> | |

+ | <li><math>F = m a</math></li> | ||

+ | </ol> | ||

− | + | '''' | |

The equation (3) can be rewritten as this(assuming that the mass supported by the wheel is equal to the total mass of the car, a poor approximation as shall be seen later on): | The equation (3) can be rewritten as this(assuming that the mass supported by the wheel is equal to the total mass of the car, a poor approximation as shall be seen later on): | ||

− | + | :<math>m a = m g k</math> | |

− | + | <ol start="5"> | |

+ | <li><math>a = gk</math></li> | ||

+ | </ol> | ||

Line 99: | Line 109: | ||

[[Image:SC-Forces.gif]] | [[Image:SC-Forces.gif]] | ||

− | As can be seen from the picture, N | + | As can be seen from the picture, N<sub>1</sub> and N<sub>2</sub> are the normal forces exerted on the car by the floor for the back and front wheel axles respectively. F<sub>1</sub> and F<sub>2</sub> <sub>g</sub> equals Mg. The system is assumed to be in an equilibrium (cases where it is not shall be discussed later on), so a balance of torques and a balance of forces are established: |

− | + | :<math>N_1 + N_2 = M g</math> | |

+ | <ol start="6"> | ||

+ | <li><math>h F_1 + h F_2 + b N_1 = (B - b)N_2</math></li> | ||

+ | </ol> | ||

− | + | Using the equation [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f5 | (5)]] F<sub>1</sub> and F'_2_' can be expressed in terms of N'_1_' and N'_2_' respectively. | |

− | + | :<math>F_1 = k_1 N_1</math> | |

− | + | :<math>F_2 = k_2 N_2</math> | |

− | |||

− | + | <sub>1</sub> and N<sub>2</sub> mostly, since they will allow us to determine the answers to the questions posed in the beginning of this section. We have a total of two unknowns and two equations (the equations for F<sub>1</sub> and F<sub>2</sub> are readily eliminated by substituting them into [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f6 | (6)]], which means that this system can be solved exactly. The equations for N<sub>1</sub> and N<sub>2</sub> are as follows: | |

− | + | :<math>N_1 = M g (B - b - h k_2) / (B + h(k_1 - k_2))</math> | |

− | + | :<math>N_2 = M g (h k_1 + b) / (B + h(k_1 - k_2))</math> | |

Let us examine these two equations. First, if one plays around with the values of the parameters one will not that it is quite easy to get negative values for one or both of these forces. Since normal forces cannot be negative, this result means that the system leaves the equilibrium and starts rotating. This implies that the car flips over. In the discussion below this aspect is ignored, but it would be unwise to ignore it when designing your car. It is unwise to let one of the axles lose its normal force entirely as well. The car relies on both of its axles to maintain its stability, and removing one of them may make the car become unstable and swerve sideways. | Let us examine these two equations. First, if one plays around with the values of the parameters one will not that it is quite easy to get negative values for one or both of these forces. Since normal forces cannot be negative, this result means that the system leaves the equilibrium and starts rotating. This implies that the car flips over. In the discussion below this aspect is ignored, but it would be unwise to ignore it when designing your car. It is unwise to let one of the axles lose its normal force entirely as well. The car relies on both of its axles to maintain its stability, and removing one of them may make the car become unstable and swerve sideways. | ||

− | Another comment is the reason why we want the expressions for these two values. When the wheels are rolling, the coefficients of friction that get plugged into the above formulas are the static kind since the contact patch between the wheel and the ground does not move. As you know from physics once the force on an object exceeds the static friction that is acting upon it, it begins to move. In this case, this would mean that the car begins to skid. This happens when the force that the brakes apply to the wheel exceeds the force of friction between the wheel and the ground. Also, from the diagram it can be clearly seen that the sum of F | + | Another comment is the reason why we want the expressions for these two values. When the wheels are rolling, the coefficients of friction that get plugged into the above formulas are the static kind since the contact patch between the wheel and the ground does not move. As you know from physics once the force on an object exceeds the static friction that is acting upon it, it begins to move. In this case, this would mean that the car begins to skid. This happens when the force that the brakes apply to the wheel exceeds the force of friction between the wheel and the ground. Also, from the diagram it can be clearly seen that the sum of F<sub>1</sub> and F<sub>2</sub> equals the total force that decelerates the car. Thus, the expressions above give us the maximum acceleration a car can have during braking. Thus it is important to maximize the normal force to be able to utilize stronger brakes and stop the car more rapidly. |

− | With that covered, let us determine which axle is the best for housing the braking system. Let us simplify the analysis by first assuming that only the front wheels have a friction coefficient. This makes N | + | With that covered, let us determine which axle is the best for housing the braking system. Let us simplify the analysis by first assuming that only the front wheels have a friction coefficient. This makes N<sub>1</sub> irrelevant (since F<sub>1</sub> becomes 0) and N<sub>2</sub> becomes: |

− | + | :<math>N_2 = M g b / (B - h k_2)</math> | |

− | + | <sub>2</sub>. This puts the center of mass as close at it can be without reducing the N<sub>1</sub> to less than 0. Thus: | |

− | + | <ol start="7"> | |

+ | <li><math>N_2max = M g (B - h k_2) / (B - h k_2) = M g </math></li> | ||

+ | </ol> | ||

− | Keeping that result in mind let us now simulate the back axle only braking system by setting k | + | Keeping that result in mind let us now simulate the back axle only braking system by setting k<sub>2</sub> to 0. As before, only the braking axle normal force matters: |

− | + | :<math>N_1 = M g (B - b) / (B + h k_1)</math> | |

In this case the maximal normal force happens when b = 0. Thus: | In this case the maximal normal force happens when b = 0. Thus: | ||

− | + | <ol start="8"> | |

+ | <li><math>N_1max = M g B / (B + h k_1)</math></li> | ||

+ | </ol> | ||

− | If we compare the equations [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f7 | (7)]] and [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f8 | (8)]] it can be seen that the bigger force occurs when the front brakes are used alone since the ratio of B / (B + h k | + | If we compare the equations [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f7 | (7)]] and [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f8 | (8)]] it can be seen that the bigger force occurs when the front brakes are used alone since the ratio of B / (B + h k<sub>1</sub>) is always smaller than 1, thus making the N<sub>1</sub>max always be smaller than N<sub>2</sub>max. Therefore, given a choice of using exclusively the front or the back axle, the front axle should be used. In this case, it is better to put the center of mass as far in the front of the car as possible without making it flip over during the braking. Also, we can examine the effects of the length of the car. If one examines the formula for N<sub>1</sub> then it can be naively thought that it does not matter. However since the numerator is will probably be less than this optimal value it is clearly seen that a large length and low height would be optimal. Experimentation is required as always, since to achieve optimal performance the knowledge of the coefficients of friction must be known. |

Note that in some cases it is impossible to have the center of mass be located anywhere near the front of the car (e.g. on a ramp scrambler). Therefore, a back axle braking system should be used. The advice on the car dimensions is identical in this case. A longer and less tall car is preferred in this case as well. There are fewer issues with a back axle braking system than a front axle system since it cannot flip over as easily, thus allowing for more optimal dimensions to be used. | Note that in some cases it is impossible to have the center of mass be located anywhere near the front of the car (e.g. on a ramp scrambler). Therefore, a back axle braking system should be used. The advice on the car dimensions is identical in this case. A longer and less tall car is preferred in this case as well. There are fewer issues with a back axle braking system than a front axle system since it cannot flip over as easily, thus allowing for more optimal dimensions to be used. | ||

− | + | <sub>1</sub> to 0, which would make a car unstable. This is not necessary in this case: any reasonable location for the center of mass will yield the maximum possible normal force. | |

To summarize then, the best braking system involves the use of both axles (or front axle only when the braking acceleration transfers close to 100% of the weight to the front axle). A car that uses such a system can be of any length and height. The next best choice is the front axle only braking system which requires a car to be long and low. The worst braking system is the back axle only kind; it requires a similar car as before. However, that being said, the front axle system is difficult to bring to optimal performance, while both back axle and all-axle systems can be easily designed to operate at optimal efficiency. | To summarize then, the best braking system involves the use of both axles (or front axle only when the braking acceleration transfers close to 100% of the weight to the front axle). A car that uses such a system can be of any length and height. The next best choice is the front axle only braking system which requires a car to be long and low. The worst braking system is the back axle only kind; it requires a similar car as before. However, that being said, the front axle system is difficult to bring to optimal performance, while both back axle and all-axle systems can be easily designed to operate at optimal efficiency. | ||

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The integrated mass scrambler is characterized by having the mass be an integral part of the scrambler car. This scrambler suffers from having to accelerate the mass it is carrying to the same speed as the car. Let us consider a physical example. As you well know, energy is conserved in a closed system. Since the goal of the event is to convert the potential energy of the mass into the kinetic energy of the car, a simple equation can be constructed: | The integrated mass scrambler is characterized by having the mass be an integral part of the scrambler car. This scrambler suffers from having to accelerate the mass it is carrying to the same speed as the car. Let us consider a physical example. As you well know, energy is conserved in a closed system. Since the goal of the event is to convert the potential energy of the mass into the kinetic energy of the car, a simple equation can be constructed: | ||

− | + | <ol start="9"> | |

+ | <li><math>PE_{mass} = KE_{car}</math></li> | ||

+ | </ol> | ||

Since the potential energy of the mass is entirely gravitational (as specifically prescribed by the rules) and the speeds involved do not come near the relativistic limits, equation 1 can be rewritten as follows: | Since the potential energy of the mass is entirely gravitational (as specifically prescribed by the rules) and the speeds involved do not come near the relativistic limits, equation 1 can be rewritten as follows: | ||

− | + | <ol start="10"> | |

+ | <li><math>m g h = 1/2 M v^2</math></li> | ||

+ | </ol> | ||

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− | + | :<math>(9.8m / s^2)(1m) = 1/2 v^2</math> | |

− | + | ||

+ | :<math>v = 4.42 m/s</math> | ||

Thus, friction aside, the best possible speed this scrambler can achieve is 4.42 metres per second. You might think that this is insanely good, but as we will later see for other scrambler types, it is far from the best you can do. | Thus, friction aside, the best possible speed this scrambler can achieve is 4.42 metres per second. You might think that this is insanely good, but as we will later see for other scrambler types, it is far from the best you can do. | ||

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The modus operandi of this device is the torque transfer from the torque provided by the falling mass, to the torque imparted on the floor surface by the wheels. The torques can be related by the simple equation: | The modus operandi of this device is the torque transfer from the torque provided by the falling mass, to the torque imparted on the floor surface by the wheels. The torques can be related by the simple equation: | ||

− | + | <ol start="11"> | |

+ | <li><math>M_g * r_1 = F_f * r_2</math></li> | ||

+ | </ol> | ||

− | ''M - the mass of the mass; r | + | ''M - the mass of the mass; r<sub>1</sub> - radius of the axle; r<sub>2</sub> - radius of the wheel; F<sub>f</sub> - force imparted onto the ground. '' |

− | The F | + | The F<sub>f</sub> force is the force that pushes the device forward. It would appear that ideally you would have a very small radius of the wheel and a very large radius of the axle to maximize the F<sub>f</sub>. However, the F<sub>f</sub> can never exceed the force of static friction that the wheels feel touching the ground. If it exceeds it, then the wheels will skid and the scrambler will not move. This places a practical limit on how small one can make the wheels. This can be helped a bit by increasing the traction between the wheels and the ground, which will allow for smaller wheels. It should also be noted that smoother force curves are preferred for this scrambler type. Often by making the F<sub>f</sub> small and thus allowing for more time for the weight to accelerate the car one can avoid the problems associated with the imperfection of the materials: if you increase the F<sub>f</sub> too much, the strings may start acting as springs. It is however difficult to predict what will happen using physics alone and thus it is advisable to test various ratios of axle to wheel radii. |

− | To improve performance, teams sometimes use variable radius axles. Generally they are set up to provide a large torque at the start to get the scrambler moving (i.e. a large r | + | To improve performance, teams sometimes use variable radius axles. Generally they are set up to provide a large torque at the start to get the scrambler moving (i.e. a large r<sub>1</sub> from equation [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f11 | (11)]]). Then as the scrambler advances, the radius of the axle decreases thus providing more acceleration, as at this point the forces of static friction are less pronounced. This fact makes theoretical predictions to be very hard for these types of devices, and thus none are provided. |

====Launcher Type==== | ====Launcher Type==== | ||

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From physics it is known that a perfectly elastic collision is simulated by the following equation: | From physics it is known that a perfectly elastic collision is simulated by the following equation: | ||

− | + | <ol start="12"> | |

+ | <li><math>v_1 = 2M / (M + m) * v_2</math></li> | ||

+ | </ol> | ||

− | ''v | + | ''v<sub>1</sub> <sub>2</sub> |

It is clear from this formula that the larger the difference between the two masses is, the faster the car will go. The limiting scenario is when the mass of the car is nonexistent, which makes it go at double the speed of the mass. We know the speed of the mass from the equation [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f10 | (10)]] when we set the big M and small m to be equal: 4.42m/s. Thus, the maximum possible speed achievable by a car launched by this launcher is an amazing 8.84m/s. | It is clear from this formula that the larger the difference between the two masses is, the faster the car will go. The limiting scenario is when the mass of the car is nonexistent, which makes it go at double the speed of the mass. We know the speed of the mass from the equation [[http://www.scioly.org/pmwiki/pmwiki.php?n=Main.Scrambler#f10 | (10)]] when we set the big M and small m to be equal: 4.42m/s. Thus, the maximum possible speed achievable by a car launched by this launcher is an amazing 8.84m/s. | ||

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The pulley launcher is one the most common launcher designs used for this event. It consists of a mass pulling a string that is redirected through a system of pulleys to pull the car. This design is popular for several reasons, it is easy to build, it is efficient and teams who use it have done well in the past. The physics of this device are covered in any decent physics class, and are simulated by the following equation: | The pulley launcher is one the most common launcher designs used for this event. It consists of a mass pulling a string that is redirected through a system of pulleys to pull the car. This design is popular for several reasons, it is easy to build, it is efficient and teams who use it have done well in the past. The physics of this device are covered in any decent physics class, and are simulated by the following equation: | ||

− | + | :<math>M g = (M + m) a</math> | |

− | + | <sup>2</sup> | |

It can be seen that by making the mass of the car small, an asymptotic acceleration of g is quickly obtained. As we know, when the acceleration is g then the maximum speed is 4.42m/s. | It can be seen that by making the mass of the car small, an asymptotic acceleration of g is quickly obtained. As we know, when the acceleration is g then the maximum speed is 4.42m/s. |

## Revision as of 02:47, 8 July 2008

## Contents

- 1 Introduction
- 2 Scoring
- 3 General Event Suggestions
- 4 General Construction Suggestions
- 5 Competition Check List
- 6 Common Mistakes and Rule Violations
- 7 Shipping and Transportation
- 8 Past Results
- 9 Useful Links

# Introduction

Scrambler is an event where teams design and build a device that transports a Large Grade A uncooked chicken egg a distance of 8 to 12 meters along a straight track as fast as possible. The device should stop as close to a terminal barrier as possible without leaving a 2 meter wide lane. The distance at the regional level will be in one meter divisions (8, 9, etc.), half meter divisions at the state level (8.0, 8.5, 9.0, etc.), and 10 cm divisions at the national level (8.0, 8.1, 8.2, etc.) . The falling mass used has a weight limit of 2 kg.

# Scoring

Score is calculated by the following formula:

- Score = 3 x (running time in seconds)+(stopping distance in cm)

Lowest score wins. The best running time of the two runs is used. Generally the stopping distance is measured perpendicularly to the wall, to the nearest millimeter. However, depending on the location of the competition sometimes measurement to the nearest decimeter can be used.

# General Event Suggestions

Firstly and arguably most importantly, **read the rules before starting to build**. There is nothing more embarrassing to a team than to be disqualified, or moved down a scoring tier, simply because they did not read the rules. Memorize the rules, have the persons who are building it be able to recite the rules verbatim, hold quizzes if necessary. Always check for clarifications on the National Science Olympiad website. When in doubt, submit a clarification request or have your coach contact the event supervisor. There is never a need to stay in the dark when it comes to the rules.

As with any building event, it is always beneficial to plan out your design before building it. Not only will it allow you to be efficient with your raw material purchases, but it may save you some embarrassing rule violations. Again, make sure to check your design against the rules.

Lastly, this event is well, extremely well, simulated by the laws of physics. This is a rarity in building events, and you should definitely take advantage of it. Talk to your physics teacher, search the internet for the appropriate physics concepts, find equations and use them. This article will attempt to introduce you to some of the concepts, but it cannot explain all of the math and analysis involved.

# General Construction Suggestions

When one looks at the scramblers in a competition, it becomes apparent that some are better built than others. At the competition, the better built scramblers tend to do better than the ones that are built poorly. Always make sure that whatever material you use is straight and sturdy, many teams failed when their cars bent out of shape by the forces of acceleration. While it often makes sense to create designs that are collapsible for easy transport, many teams that used such designs were plagued by loose tolerances that were imposed on them, often failing to have their scrambler stay in the 2 meter lane. If you use wood, always use screws and glue, never use nails. If you use metal construction kits, make sure everything fits.

You must always balance your construction style between adjustability and stability. Covering every joint with glue may seem like a good idea, but it will make your design be very rigid and unchangeable. Adjustability is very important, as few get their designs to be perfect on the first try, and you should always consider that when choosing a bonding method. In theory, it is always possible to add an extra pair of screws, or even add a nut and bolt fastener and achieve the same stability as a dab of glue. When in doubt, and where weight does not matter, choose fasteners instead of glue.

## Course Deviation

Having a scrambler that runs straight and true is very important, within limits. A 10cm deviation from center over a 10m course is caused by being just 0.57 degrees off course. Half a degree accuracy is more than can be reasonably expected at competition. Course deviations can cause problems with breaking accuracy by changing the distance between the launcher and the wall. Luckily, at 10m, a deviation of 14.1cm results in a change of only 1mm in the distance.

## Common Components

While varied, most devices used for this event share some general parts.

### Wheels

*Physical Considerations*

The wheel is one of the most critical components of a scrambler. There are several properties of the wheel that are important to consider for the purposes that it is used in this event. The wheels mass, or more appropriately, its rotational inertia is one of the important of those properties. As we know from physics, the resistance to acceleration in a linear motion is different from the resistance to acceleration in a rotational motion. It is notable that the wheel in a scrambler is a rolling object, and thus it is a great mistake to ignore both components of its motion. It is a well known derivation from physics that the total energy of the rolling wheel is:

Note that radial velocity is easily related to the normal velocity of the wheel(and thus the car it is attached to by a simple equation:

It can be noted that the increase in mass, radius and rotational inertia all will lead to the wheel storing more energy in it that can be better used to accelerate the car. Note that the radius term is squared, so any increase in the wheels radius will severely impact its energy properties. Lastly, the inertial component is very often dependent on the squared radius of the wheel as well, further increasing the importance of the radius of the wheel.

Note, that nothing has been said whether having a large mass of the wheel is bad or good. This question cannot be answered decisively in either direction. Smaller mass wheels (i.e. wheels that are small and light) allow for your scrambler to go faster, but they will also have to spin faster and thus are very susceptible to axle friction. Many teams with tiny wheels failed to reach the wall simply because the cars, while launched at respectable speed, were bogged down by friction. Ways to reduce this friction will be discussed shortly. Teams with large wheeled scramblers enjoy lumbering, but roughly constant speeds. Once you accelerate the beast of a lawnmower wheel, it will not want to stop for a while. Note that the wheel radius is of a particular importance to one of the integrated mass scrambler types; that will be discussed later.

*F _{f<}*

The equation (3) can be rewritten as this(assuming that the mass supported by the wheel is equal to the total mass of the car, a poor approximation as shall be seen later on):

[| (3)][| (5)] is largely valid: the only way to increase the traction of the wheel is to increase its coefficient of friction. With the theory covered, let us now discuss the material considerations of the wheels.

*Material Considerations*

Physics is all nice and good, but given the limited budgets of most teams it has to be eclipsed by the availability of the materials. Most teams use some sort of pre-made disks for their wheels, a common sight are CD/LP based wheels. Roller blade wheels are often visible as well. Better funded teams may wield custom made acrylic wheels, or even those cut from sheets of balsa. Harking to the first property of a wheel discussed above lighter wheels are generally better, and thus teams go to great lengths to lighten their wheels. Given good drilling equipment it is advisable to drill a series of holes in the wheel to make it lighter. Take care to do it in a symmetrical fashion, and not to weaken the wheel too much. Note that from equation [| (1)] it can be seen that the greatest effect shall be seen from reducing the weight of the rims of the wheel. And as always, look at the professional wheels for guidance, high-speed bicycles often have very efficient designs for their wheels.

To reduce the axle friction teams use ball bearings. These gadgets, while sometimes expensive and tough to find, will often nullify any problems associated with small wheels. Keep these free from dust and well lubricated with grease or other lubricant.

For traction many teams use rubber bands around their wheel rims, some use latex gloves as a faster and easier alternative. Latex tubing slit lengthwise also makes a good traction enhancer. The rules prohibit any lasting glues from being used for traction purposes, so take care not to use anything like that.

### Brakes

While some teams cannot even get their scrambler to travel the announced distance, those that do face the problem of the egg traveling more than the 1 m/s (average upper limit for the speed that the egg can survive decelerating from) towards a very solid wall. Generally, a brake is used.

*Physical Considerations*

While the equation [| (5)] is a good approximation for a single wheel scrambler, such things are a rarity. A more careful analysis is required. There are four main questions that must be considered during the design of a braking system of a scrambler: how long to make the car, where to put the center of mass, which wheels(front versus back) work better for braking and how to avoid skid. To answer these questions, we shall consider a simple model for a braking car.

As can be seen from the picture, N_{1} and N_{2} are the normal forces exerted on the car by the floor for the back and front wheel axles respectively. F_{1} and F_{2<g equals Mg. The system is assumed to be in an equilibrium (cases where it is not shall be discussed later on), so a balance of torques and a balance of forces are established:
}

Using the equation [| (5)] F_{1} and F'_2_' can be expressed in terms of N'_1_' and N'_2_' respectively.

_{1} and N_{2} mostly, since they will allow us to determine the answers to the questions posed in the beginning of this section. We have a total of two unknowns and two equations (the equations for F_{1} and F_{2} are readily eliminated by substituting them into [| (6)], which means that this system can be solved exactly. The equations for N_{1} and N_{2} are as follows:

Let us examine these two equations. First, if one plays around with the values of the parameters one will not that it is quite easy to get negative values for one or both of these forces. Since normal forces cannot be negative, this result means that the system leaves the equilibrium and starts rotating. This implies that the car flips over. In the discussion below this aspect is ignored, but it would be unwise to ignore it when designing your car. It is unwise to let one of the axles lose its normal force entirely as well. The car relies on both of its axles to maintain its stability, and removing one of them may make the car become unstable and swerve sideways.

Another comment is the reason why we want the expressions for these two values. When the wheels are rolling, the coefficients of friction that get plugged into the above formulas are the static kind since the contact patch between the wheel and the ground does not move. As you know from physics once the force on an object exceeds the static friction that is acting upon it, it begins to move. In this case, this would mean that the car begins to skid. This happens when the force that the brakes apply to the wheel exceeds the force of friction between the wheel and the ground. Also, from the diagram it can be clearly seen that the sum of F_{1} and F_{2} equals the total force that decelerates the car. Thus, the expressions above give us the maximum acceleration a car can have during braking. Thus it is important to maximize the normal force to be able to utilize stronger brakes and stop the car more rapidly.

With that covered, let us determine which axle is the best for housing the braking system. Let us simplify the analysis by first assuming that only the front wheels have a friction coefficient. This makes N_{1} irrelevant (since F_{1} becomes 0) and N_{2} becomes:

_{2}. This puts the center of mass as close at it can be without reducing the N_{1} to less than 0. Thus:

Keeping that result in mind let us now simulate the back axle only braking system by setting k_{2} to 0. As before, only the braking axle normal force matters:

In this case the maximal normal force happens when b = 0. Thus:

If we compare the equations [| (7)] and [| (8)] it can be seen that the bigger force occurs when the front brakes are used alone since the ratio of B / (B + h k_{1}) is always smaller than 1, thus making the N_{1}max always be smaller than N_{2}max. Therefore, given a choice of using exclusively the front or the back axle, the front axle should be used. In this case, it is better to put the center of mass as far in the front of the car as possible without making it flip over during the braking. Also, we can examine the effects of the length of the car. If one examines the formula for N_{1} then it can be naively thought that it does not matter. However since the numerator is will probably be less than this optimal value it is clearly seen that a large length and low height would be optimal. Experimentation is required as always, since to achieve optimal performance the knowledge of the coefficients of friction must be known.

Note that in some cases it is impossible to have the center of mass be located anywhere near the front of the car (e.g. on a ramp scrambler). Therefore, a back axle braking system should be used. The advice on the car dimensions is identical in this case. A longer and less tall car is preferred in this case as well. There are fewer issues with a back axle braking system than a front axle system since it cannot flip over as easily, thus allowing for more optimal dimensions to be used.

_{1} to 0, which would make a car unstable. This is not necessary in this case: any reasonable location for the center of mass will yield the maximum possible normal force.

To summarize then, the best braking system involves the use of both axles (or front axle only when the braking acceleration transfers close to 100% of the weight to the front axle). A car that uses such a system can be of any length and height. The next best choice is the front axle only braking system which requires a car to be long and low. The worst braking system is the back axle only kind; it requires a similar car as before. However, that being said, the front axle system is difficult to bring to optimal performance, while both back axle and all-axle systems can be easily designed to operate at optimal efficiency.

It should be noted that having extremely high coefficients of friction will make even suboptimal brake geometry perform well. By using rule-compliant adhesive surfaces(that leave no residue on the floor), such high coefficients can be generated, that the car may stop nearly instantaneously. This makes the choice of location for the brake pad (wheel based brakes cannot easily utilize adhesives) less important. The analysis above will still apply: less adhesive surface will be needed for a brake pad in the front of the car then a pad in the rear. Note that this seems to go against the caution against skidding above. The caution still applies, as the coefficient of friction for the adhesive pad will vary on various surfaces. However, since it is so high, the variation should not bring about the onset of the actual skidding, thus removing the issues of consistency.

One final point. The length of the car in these calculations was measured from axle to axle, which implies that the actual car length does not matter all that much. That is, if your car has a short wheel base but a long rod behind it(which was say used during the launching process) the car is still short in terms of the analysis above.

#### Braking Systems

There are three commonly used braking systems. Here they are listed in order of difficulty of construction.

##### String Type

*Pros*

- Easy to build

*Cons*

- Poor Accuracy
- Backlash
- Skid

The first braking design is made by running a string from one axle to another. As the car travels, the string from one axle unwinds and wraps around the second axle. Once all of the string has fed through from one axle to the another the axles lock and the car stops. The distance the car travels can be controlled by the amount of string wrapped around each axle. This design tends to have poor accuracy for several reasons. First, the string used will often stretch in an irregular way. Second, the string will not always wrap in exactly the same manner, meaning there is a slight variation in the amount of travel allowed before stopping the car. Third, while the taut string will prevent the car from moving forwards, nothing prevents the car from moving backwards. So, you will get some amount of backlash.

##### Threaded Rod Type

*Pros*

- High accuracy
- Consistency
- No Backlash

*Cons*

- Somewhat complicated to build
- Skid
- Added friction to the axles

This system is very popular among competitors. While only slightly more complicated than the string method, it is more consistent. The basic concept of this design is using a threaded rod for the axle, placing a nut (usually a wing nut is used) on the axle. As the wheels rotate the rotating motion is transferred in to horizontal motion of a wing nut moving it along the axle. When the wing nut reaches a barrier, it will no longer be able to move, and thus stops the axle from turning. The distance is set by setting how far the wing nut starts from the barrier and is usually measured in rotations of the wheels. While as described the system is still vulnerable to skid, it can be minimized by carefully choosing a material for the barrier that the wing nut engages during the stopping motion. By choosing something rubbery many teams achieved a gradual locking of the wheels, which effectively eliminated any skid inherent to the system. The wing nut also adds some friction to the axle, thus the car may not roll as smoothly or as far.

##### Brake Pad Type

*Pros*

- High accuracy
- Consistency
- Reduced skid

*Cons*

- Most complicated to make
- Adds friction to the axles

This braking system introduces a braking surface, or pad, that is used to stop the car. Unlike the other two designs, there is no standard method of constructing this design although most of them are based on the threaded rod braking system. The concept of this design begins the same as that of the threaded rod design, but rather than relying on the wing nut to jam the wheels and slow the car to a halt, it uses the wing nut to somehow trigger the lowering of the braking pad. The actual methods that the teams use to accomplish this varies, some rely on the wing nut to pull out a restraining pin directly, others have it be pushed aside through a system of levers. By adding a surface that can in theory have a greater coefficient of friction than the wheel rims, the stopping performance can be improved. As the brake pad can be located anywhere on the car, the braking efficiency can be maximized, leading to many of these designs to be able to stop almost instantly without any skid. Another advantage of this method is that attempting this design carries a fairly low risk, because it can be reduced to the basic threaded rod design fairly easily if you cannot get the system to work.

### Mass Release Mechanism

While optional, some teams like to use mass release mechanism to improve the consistency of their scramblers. Its use negates the necessity of steady hands of the person who is handling the mass, and allows for near constant launch speeds. This generally improves the performance of brakes that are strongly dependent on the speed of the scrambler, such as the wing-nut braking mechanism. A common design for such a device is a pin system, where the mass is suspended on a pin that can be pulled out to produce a consistent release of the mass.

### Rollers

Many of these designs involve rollers that redirect strings. They are commonly referred to as pulleys as well, although that is somewhat dubious. The important consideration for these devices is their friction, or rather, its absence. This cannot be the case if the roller does not contain a bearing in it. The advantage of a bearing is that the friction remains roughly constant irrespective of the load that the roller is forced to bear. If a bearing is absent, then the equation [| (3)] applies, which can prove catastrophic is large tensions are used (this assumes an unlubricated bearing, with a lubricated bearing the friction will decrease once the speed of the bearing surfaces is high enough to cause hydrodaynamic forces to float the bearing surfaces apart). You can easily test whether a roller has a bearing in it or not. Take a string and try using the roller to redirect the string while pulling on it. If when varying the tension the resistance also varies, then there is no bearing in that roller. Avoid it and buy a roller that has one.

### Bearings

As discussed above, bearings are constant (low) friction devices. They are indispensable in rollers, and often are very helpful to hold axles of wheels (especially for the small wheels). The best bearing for this event would be a radial bearing, with caged balls. It is also preferable to have it be free of the side shields: it is easy for teams to keep them dust free, and by lubricating them regularly the low friction can be maintained very easily.

### Device Systems

This event is known for the variety of devices that can be used to accomplish the task. They can be subdivided into two main categories. The integrated mass scramblers have the car always stay in contact with the weight, sometimes it is used to accelerate the car throughout the run, or sometimes it is simply not discarded as means to simplify the design. The other main type is the launcher systems which consist of a car that is separate from a launcher, which contains the machinery to use the mass to accelerate the car.

#### Integrated Mass Type

*An Introduction from Physics*

The integrated mass scrambler is characterized by having the mass be an integral part of the scrambler car. This scrambler suffers from having to accelerate the mass it is carrying to the same speed as the car. Let us consider a physical example. As you well know, energy is conserved in a closed system. Since the goal of the event is to convert the potential energy of the mass into the kinetic energy of the car, a simple equation can be constructed:

Since the potential energy of the mass is entirely gravitational (as specifically prescribed by the rules) and the speeds involved do not come near the relativistic limits, equation 1 can be rewritten as follows:

[| (10)] cancel, and we can solve for the v.

Thus, friction aside, the best possible speed this scrambler can achieve is 4.42 metres per second. You might think that this is insanely good, but as we will later see for other scrambler types, it is far from the best you can do.

##### Ramp Scrambler

*Pros*

- Easy to build
- Good theoretical performance
- Performance largely independent of the mass used

*Cons*

- Theoretical performance difficult to achieve
- Often difficult to fulfill the egg on the starting line requirement

*(Note that the entire car is counted as the mass during impoundment)*

This integrated mass scrambler consists of a car with a mass attached to it that rolls down a ramp and continues onto towards the wall. This scrambler is very accurately approximated by the equation [| (10)]. This scrambler is arguably the easiest one to build, although it always runs into the trouble when putting the front of the egg on the start of the line. This can is often avoided by using very long cars. It is well known from the derivations by Newton et al that the ramp shape that allows for a mass to descend in the shortest time, a brachistochrone, is a 4 pointed astroid. This curve is difficult to get perfect, and through some calculations it can be seen that pretty much any curve that approximately looks like a quarter circle will do just as well. Note that from physics it is known that the car will do best if its mass is concentrated in the back (thus starting higher on the ramp). This presents many problems for braking, as discussed in the braking section above, as this is exactly the opposite of what is desired for a front braking car. However, there are teams that do well with this design, and it represents a valid choice.

Note that this scrambler is often classified as a launcher type, citing the fact that the ramp acts as a launcher, and that this type was not allowed by the rules from years that did not allow for multipart launchers. However, this scrambler obeys the equation [| (10)] which takes precedence.

Here are some numbers that can be calculated from simple physics. These calculations assume a perfect design and no friction. Distance is set at 10 metres. The mass of the car is set at the mass of the weight. They also assume that all of the mass of all three vehicles is centered at the same single point in space, actually the more massive vehicles are likely to have a higher center of mass so they would actually exit the launcher at a higher speed. [| '^*^']

Mass | Idle Time | Acceleration Time | Exit Speed | Travel Time | Total Time |
---|---|---|---|---|---|

0.5 kg | 0.00 sec | 0.59 sec | 4.43 m/s | 2.57 sec | 3.16 sec |

1.0 kg | 0.00 sec | 0.59 sec | 4.43 m/s | 2.57 sec | 3.16 sec |

2.0 kg | 0.00 sec | 0.59 sec | 4.43 m/s | 2.57 sec | 3.16 sec |

**A note about these and future numbers:*#note
The car assembly(car and the egg) are assumed to weigh 150 grams(unless stated otherwise). The brake is assumed to be instantaneous. The distance is assumed to be 10 meters. Note that these values will never be achieved, since they assume no friction and mildly unrealistic design choices, but the patterns can still be observed and the inter-type comparison can still be made.
The idle time represents the time needed for the device to prepare itself, be it cocking of the spring in the spring launcher, or the falling of the hammer in the hammer launcher. The acceleration time column represents the time the device spends accelerating the car; this is different from the idle time because the car is actually moving during this point. The exit speed represents the speed at which the car is moving after it leaves the launcher. The travel time is the time the car takes to travel the distance from the launcher to the wall(this may or may not equal to the assumed distance of 10 meters, since some launchers push the car forward of the starting line as part of their acceleration routine). The three rows signify the masses of the weight that is used to power the device.

##### Tower Scrambler

*Pros*

- Reasonably easy to build
- Good theoretical performance

*Cons*

- Theoretical performance impossible to achieve, so much so that often the required distance cannot be covered
- Manufacture of the variable radius axles can be challenging
- Severe dependence on mass used

A relic of the times when only single part devices were allowed, this integrated mass launcher consists of a car that is propelled by a falling mass that uses a pulley system or otherwise to directly convert the motion of the weight into the motion of the car. This scrambler obeys the equation [| (10)] reasonably well. However, the approximation of equating the mass of the car to the mass of the mass is impossible to make in this case. The support structure for the mass and the pulley system (not to mention the wheels) often drive the masses of these scramblers above 5 kilograms. This makes these scramblers very slow. As such, many teams have great trouble of getting the scramblers to cover the whole distance.

Unique to this design is a braking system that involves the mass simply hitting the ground, perhaps assisted by a braking pad. This brake is severely dependent on the speed of the scrambler, which in part is dependent on the surface of the scrambler, making it unreliable for close-to-wall stopping.

The modus operandi of this device is the torque transfer from the torque provided by the falling mass, to the torque imparted on the floor surface by the wheels. The torques can be related by the simple equation:

*M - the mass of the mass; r _{1} - radius of the axle; r_{2} - radius of the wheel; F_{f} - force imparted onto the ground. *

The F_{f} force is the force that pushes the device forward. It would appear that ideally you would have a very small radius of the wheel and a very large radius of the axle to maximize the F_{f}. However, the F_{f} can never exceed the force of static friction that the wheels feel touching the ground. If it exceeds it, then the wheels will skid and the scrambler will not move. This places a practical limit on how small one can make the wheels. This can be helped a bit by increasing the traction between the wheels and the ground, which will allow for smaller wheels. It should also be noted that smoother force curves are preferred for this scrambler type. Often by making the F_{f} small and thus allowing for more time for the weight to accelerate the car one can avoid the problems associated with the imperfection of the materials: if you increase the F_{f} too much, the strings may start acting as springs. It is however difficult to predict what will happen using physics alone and thus it is advisable to test various ratios of axle to wheel radii.

To improve performance, teams sometimes use variable radius axles. Generally they are set up to provide a large torque at the start to get the scrambler moving (i.e. a large r_{1} from equation [| (11)]). Then as the scrambler advances, the radius of the axle decreases thus providing more acceleration, as at this point the forces of static friction are less pronounced. This fact makes theoretical predictions to be very hard for these types of devices, and thus none are provided.

#### Launcher Type

*An Introduction from Physics*

Launcher type scramblers without exception are characterized by the existence of a device separate from the car that is designed solely for the purpose of converting the potential energy of the mass into the kinetic energy of the car. This, unsurprisingly, means that means that this type of scrambler is easily simulated by the equation [| (10)]. The advantage that these systems possess over the integrated mass scrambler type is that the little m in that equation can be smaller than the big M.

##### Spring Launcher

*Pros*

- Nearly maximum theoretical efficiency possible in a scrambler
- Reasonably easy to achieve the theoretical performance
- Low dependence on mass used

*Cons*

- The locking mechanisms are often difficult to build
- Complexity of the device requires careful construction
- Rapid speed of the car makes it difficult to stop

Spring launcher is one of the rarest launcher scrambler types, often sighted alone in competitions. Being a very complicated design, it is often mis-built by teams, and thus gets a bad reputation. However, it easily achieves the highest speeds for scrambler cars, at all distances and most masses.

Its mode of operation is simple in theory. The mass first stores its potential energy in some sort of elastic medium, be it a spring or a rubber band, which then is released to accelerate the car. This decoupling of the mass and the car allows for the equation [| (10)] to be obeyed very closely. M does indeed represent solely the mass of the mass, m does indeed represent solely the mass of the car. It is there that the speed of this launcher lies, as one makes the mass of the car smaller, no limiting speed is approached, unlike other scrambler types.

In practice, however, the above is difficult to build. Some teams use masses attached to arms with slits in them that allow for a looped string to slip and release the spring once a particular angle is attained by the arm. Some teams build a more sophisticated system of coupled locks (as depicted in the diagram) to mediate the energy transfer.

Superficially, a true spring launcher is very similar to a pulley launcher, and thus if the spring experiment fails, it can be easily down-graded to a functioning pulley launcher. When operating this launcher, teams often observe a noticeable time spent on the launcher charging itself up (performing the energy transfer from the mass to the spring). This can be disconcerting, but often the speed obtained makes up the difference. This property makes the spring launchers behave better at longer track lengths.

Another problem unique to this launcher is that the car is launched at such a great speed, that most brakes used for other, slower, launchers are inadequate for this design. Due to the rarity of this design no general solution to this problem has been posed, but theory does not forbid a solution from existing.

The following are some numbers derived from physics. Note that this launcher pushes the car forward 1 meter before it is set free.[| '^*^']

Mass | Idle Time | Acceleration Time | Exit Speed | Travel Time | Total Time |
---|---|---|---|---|---|

0.5 kg | 0.71 sec | 0.19 sec | 8.80 m/s | 1.11 sec | 2.02 sec |

1.0 kg | 0.71 sec | 0.14 sec | 11.43 m/s | 0.79 sec | 1.63 sec |

2.0 kg | 0.71 sec | 0.10 sec | 16.17 m/s | 0.56 sec | 1.36 sec |

##### Hammer Launcher

*Pros*

- High theoretical efficiency
- Very easy to build

*Cons*

- High dependence on mass used
- Theoretical efficiency is difficult to achieve, due to the non-truly elastic collisions
- The rapid acceleration is stressful on the car, requiring it to be sturdy

Hammer launcher is one of the easiest launchers you can build. It consists of a pendulum hammer falling and smashing a car from the behind. The momentum is exchanged, and the usually light car is accelerated to high speeds.

From physics it is known that a perfectly elastic collision is simulated by the following equation:

*v _{1<2<}*

It is clear from this formula that the larger the difference between the two masses is, the faster the car will go. The limiting scenario is when the mass of the car is nonexistent, which makes it go at double the speed of the mass. We know the speed of the mass from the equation [| (10)] when we set the big M and small m to be equal: 4.42m/s. Thus, the maximum possible speed achievable by a car launched by this launcher is an amazing 8.84m/s.

That speed however is unattainable, since the car cannot be massless and the collision involved is seldom perfectly elastic. Light cars can easily alleviate the first problem. The second problem is solved in various ways by teams. By varying the materials at the contact position the elasticity of collisions can be enhanced. Many teams have trouble keeping their small car from launching at an angle. Some teams did manage to negate this problem by using longer cars that have the hammer hit a patch that is located in between their wheels.

The mass of the entire arm must be weighed during the impounding, since most designs have the arm lose it potential energy as a whole. From physics it is known that to achieve optimum efficiency, most of the mass of the arm must be concentrated into its distal end, thus making most teams using a hammer/mallet like arrangement. Here are some theoretical data.[| '^*^']

Mass | Idle Time | Acceleration Time | Exit Speed | Travel Time | Total Time |
---|---|---|---|---|---|

0.5 kg | 0.59 sec | 0.00 sec | 6.81 m/s | 1.46 sec | 2.06 sec |

1.0 kg | 0.59 sec | 0.00 sec | 7.70 m/s | 1.29 sec | 1.89 sec |

2.0 kg | 0.59 sec | 0.00 sec | 8.24 m/s | 1.21 sec | 1.81 sec |

##### Pulley Launcher

*Pros*

- Good theoretical efficiency
- Easy to achieve theoretical efficiency
- Simple construction

*Cons*

- Some dependence on mass used

The pulley launcher is one the most common launcher designs used for this event. It consists of a mass pulling a string that is redirected through a system of pulleys to pull the car. This design is popular for several reasons, it is easy to build, it is efficient and teams who use it have done well in the past. The physics of this device are covered in any decent physics class, and are simulated by the following equation:

^{2<
}

It can be seen that by making the mass of the car small, an asymptotic acceleration of g is quickly obtained. As we know, when the acceleration is g then the maximum speed is 4.42m/s. The fact that this launcher involves no true energy transfers, any deviation from theoretical performance is explained away by friction in the rollers and wheels. Since those can be easily fixed, these scramblers are often the faster half of launchers in any given competition.

Here are some theoretical data from physics. Note that this launcher pushes the car 1 metre before releasing it.[| '^*^']

Mass | Idle Time | Acceleration Time | Exit Speed | Travel Time | Total Time |
---|---|---|---|---|---|

0.5 kg | 0.00 sec | 0.51 sec | 3.88 m/s | 2.32 sec | 2.83 sec |

1.0 kg | 0.00 sec | 0.48 sec | 4.13 m/s | 2.18 sec | 2.66 sec |

2.0 kg | 0.00 sec | 0.47 sec | 4.27 m/s | 2.11 sec | 2.57 sec |

##### Push Rod Launcher

*Pros*

- Simple construction

*Cons*

- Poor theoretical efficiency
- Difficult to achieve the theoretical efficiency

A common design for a launcher, this launcher is seen in large numbers in some competitions. There is no reason for this popularity however, this launcher cannot be better than a pulley launcher, and as shall be shown it is worse. The launcher consists of a hammer arm akin to the one from a hammer launcher connected by a rod to the car. Thus as the hammer swings down, the car is pushed forward by the rod.

The physics of this system are highly complicated, and cannot be simulated by high school physics, thus any theoretical analysis will have to be gleaned from the theoretical data at the end of this section.

Practically speaking, the difficulty in attaining the theoretical efficiency of this launcher lies in the fact that both the arm and the rod are not massless, and by diluting the concentration of the mass at the distal end of the arm, they quickly reduce the efficiency of this launcher. As always, the entire mass of the arm and rod assembly must be weighed during the impoundment. Here are some theoretical data for this launcher. Due to the rod length, the car is pushed a full 1.4 metres forward before being released.[| '^*^']

Mass | Idle Time | Acceleration Time | Exit Speed | Travel Time | Total Time |
---|---|---|---|---|---|

0.5 kg | 0.00 sec | 0.66 sec | 3.88 m/s | 2.21 sec | 2.87 sec |

1.0 kg | 0.00 sec | 0.63 sec | 4.13 m/s | 2.08 sec | 2.71 sec |

2.0 kg | 0.00 sec | 0.61 sec | 4.27 m/s | 2.01 sec | 2.62 sec |

# Competition Check List

Be sure to bring the following items to competition with you.

- The scrambler car, and all accompanying parts
- Extra mass
- Tools
- Spare parts
- Glue and tape
- A metric tape measurer

Also, upon arrival to competition, be sure to make a few pre-runs to verify that everything works. Also, it is helpful to judge the quality of the surface at the competition location, and use that information during the setting of the brakes.

# Common Mistakes and Rule Violations

Most of the teams at the regional and state level get disqualified for out of spec designs. But, since you have read this guide and memorized the rules, you should not be one of them. Make sure that your scrambler's design is so that when you launch, the egg's front is in line with the starting line. You may not start with the egg behind the line. If your scrambler cannot make half the announced distance, your run is counted with a rule violation. If you use a mass from a balance set, and you add a hook to it, make sure to check that it is still within rule limitations, as the hook may add mass. Your scrambler is not allowed to have any stored energy that will add to the propulsion of your device. For example, mousetrap cars are not allowed. The rules, however, allow for stored energy to be used in a braking system.

When setting up to launch, you will need to do 4 things in some order: attach the egg to the car, position the car in the launcher, attach the mass, and adjust the braking mechanism for the proper distance. You should think ahead of time about what order to do these things in. For example, if you wind the wheels and then they rotate as you roll the car into the launcher, you will end up either long or short.

Also, some teams drop the egg and crack it while trying to attach it to the car--this knocks the team out of the running! Work on attaching the egg at ground level, not waist level. Consider bringing a foam pad to sit under the car/egg while you're attaching the egg.

# Shipping and Transportation

Be sure to provide a sturdy crate for your scrambler car if your team has to travel to competitions. A half inch plywood box should be sufficient. Be sure to provide necessary padding so that the scrambler does not get damaged. Also, just in case something does get damaged, make sure to bring enough extra supplies (and tools) to be able to fix most conceivable breakages.

# Past Results

## 2007 National Results from top 3 teams

Announced Distance: 8.7 meters

School | Time | Stopping Distance | Total Score |
---|---|---|---|

Grand Haven, MI | 3.53 seconds | 0.4 cm | 10.99 |

Wichita Collegiate, KS | 2.90 seconds | 2.6 cm | 11.30 |

Newton North, MA | 3.34 seconds | 2.0 cm | 12.02 |

## 2006 National Results from top 3 teams

Announced Distance: 8.1 meters

School | Time | Stopping Distance | Total Score |
---|---|---|---|

Harriton, PA | 3.00 seconds | 0.8 cm | 9.8 |

Troy, CA | 3.56 seconds | 0.0 cm | 10.68 |

Randolph, AL | 3.53 seconds | 0.3 cm |

## 2000 National Results from top 3 teams

School | Predicted Distance | Actual Distance | Time | Stopping Distance | Total Score |
---|---|---|---|---|---|

Maine-Endwell, NY | 868.0 cm | 868.40 cm | 5.21 seconds | 3.00 cm | 19.83 |

J. T. Hoggard, NC | 864.0 cm | 865.90 cm | 5.94 seconds | 3.80 cm | 27.32 |

Maize, KS | 860.0 cm | 859.70 cm | 5.13 seconds | 11.70 cm | 27.99 |