## The fins

andrewwski
Posts: 954
Joined: January 12th, 2007, 7:36 pm
Has thanked: 0
Been thanked: 11 times

### Re: The fins

Zioly wrote:
Agreed. The science behind it is precise and at times overwhelming. However, I believe there's a portion of the fins' impact that you have acknowledged, but overlooked, in my opinion. That impact is the drag the fins create on the descent. Large fins will slow the rocket's descent exponentially compared to the slight increase in distance with smaller fins.
Yes - naturally, the characteristics which you want during descent are exactly the opposite of what you want during ascent. However, I'd take exception with your assessment that "large fins will slow the rocket's descent exponentially compared to the slight increase in distance with smaller fins." Careful using words such as "exponentially" without corresponding analysis or theory to back them up.

Let's look at the equation for drag:

$F_d=\frac{1}{2}\rho V^2 C_D A$

where $\rho$ is the air density, $V$ is the velocity of the air stream, $C_D$ is the coefficient of drag, and $A$ is the reference area, or the cross-sectional area perpendicular to the flow.

If we assume that the flight is always in a fixed direction, traveling with the nose forward and nozzle aft, then the area and drag coefficient can be assumed to be constant throughout the flight. Note that this doesn't exactly hold at apogee, when the rocket tips over, but the velocity is quite low here, so the impact of the drag is rather low. Air density can be assumed constant.

Then, we see that drag is entirely dependent on the square of the velocity. So the faster the object is going, the more drag force it is subject to. So let's ask the question - when is the rocket at its fastest velocity? Naturally, this is during the short period in which the water and air are being expelled - or on the way up!

Now, using larger fins in the direction along the rocket's long axis doesn't actually increase $A$, but it does increase $C_D$. Either way, both of these quantities have a linear effect on velocity, so we can group them together.

So we see that during the ascent, both drag and gravity act in the same direction, while during the descent, drag acts in the opposite direction of gravity. If there were no drag, we would expect the velocity at launch and the velocity at impact to be the same. But since there is drag, we know the velocity at impact must be slower than the velocity at launch. Since drag forces are proportional to the square of velocity, we know they will be greater on ascent than on descent!

But, this has assumed that the mass of the rocket is constant, and that all of the ascent velocity is initial, i.e. it disregards the acceleration period when the water is being expelled. This is probably an OK assumption, as the water is expelled rather quickly. However, it does mean that the initial mass is significantly higher, and the initial velocity is significantly lower, and this serves to lower the effects of drag initially. Is this enough to make a high-drag design advantageous? With the quick acceleration, intuition says not - but never trust intuition over analysis!

This site gives not only the equations of projectile motion, but also the equations for the evolution of the internal mass (i.e. air/water expelling from the pressure vessel):

http://www.sciencebits.com/RocketEqs

They've nicely put together a simulator which integrates these equations forward to plot the trajectory:

http://www.sciencebits.com/RocketCalcul ... omForm=yes

You can input your own parameters into this. Try a few constant values of everything except $C_D$. Then, you'll see that as you increase $C_D$, the apogee altitude decreases and the flight becomes shorter.

This shows that in these simulated cases, the above assumption is valid, and that drag has a greater effect on ascent, as would be expected. So we can conclude that we want to minimize drag to increase flight time!

Note that the above analysis has assumed a statically stable rocket, which will nosedive after apogee. As I mentioned previously, if you can change the drag characteristics for descent versus ascent, you can increase the flight time. This is the advantage to the "backslider."
While it's true that the fins control the CG, CP, and other things such as CLA, the applications of these are strictly limited to, in my opinion, whether the rocket will nose-dive or not and whether it'll fly straight or not. Once a rocket have achieved a simple ascent, flip at apogee, and horizontal descent, the next step it to try to maximize the time upon that simple structure.
Aha - again, careful! Opinions are meaningless without data to support them, and conclusions should be drawn based on theory, analysis, and experimentation.

Now, you're correct that the CG, CP, CLA will control whether the rocket nose-dives or flies straight (those are characteristic of a stable rocket). But, as I mentioned in a previous post - if you can build a design that exploits changes in these during flight, then you can add more drag on the way down than the way up. This is what the "backslider" does.
So, if the "simple structure" or that formula was created with CG, CP, and CLA calculations, the next bit is moreso strategy and "weighing the benefits." For example, small fins will make the rocket fly higher, but they also won't create as much drag as larger fins would. Larger fins would cause a rocket to lose some altitude, but ultimately, well-built large fins will entail a very slow descent.

In my opinion, it's the descent that matters--not how high a rocket goes. A slow descent is exponentially more impactful on time than a slightly higher altitude. That being said, your original point is still valid: balance. For example, as you said, it's important to strike a balance between large fins and small fins to ensure that the rocket does in fact stay stable, but that's merely the surface of this great event.
Again, careful with opinions - opinions without justification have no place in science!
In my haste, I probably overlooked the fact that others might not have had experience properly balancing a rocket without calculations, so that it's practically second nature, but when I said that bigger fins were better, I meant that the strategy they promoted ultimately led to higher times. Additionally, my tip meant to focus on larger fins and to perfect them.

I hope I didn't ramble on too badly and that my point was made clear. If not, please ask, and I'd be more than happy to answer any questions and clear up any confusion. Also, I was in no way discrediting your post, andrewwski; I was just giving my own insight on the strategy of the fins.
Don't ever worry about discrediting a post, or sharing your thought process and conclusions. This is the foundation of science - discussion and rebuttal is critical! But, at the same time, conclusions without analysis won't get you very far - so careful making assertions unless you can back them up!

Member
Posts: 111
Joined: March 31st, 2016, 3:28 pm
Division: C
State: PA
Location: Mariana Trench
Has thanked: 0
Been thanked: 0

Zioly wrote: