# Determining apogee without using Rocsim?

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#### tpw2000

##### Member
Hello all, I'm new to the forum but not so much to rockets. I've mostly been flying low-power Estes kits for a while, making small scratch builds with C6-5's and was looking to step up my game a bit, getting into composite motors. Is there a set of formulas I can use to determine velocity and vertical apogee? It's been a couple years since physics (I'm a senior, just recently able to buy composite reloads) but if anyone knows the mathematical formulas to find drag coefficient it would be very helpful. Thanks in advance!!

OpenRocket is like RockSim, but free. Not all features all supported (like tube- and ring-fins), but it's great with standard rockets.

Also, you can get a good, basic sim for the purposes of altitude and delay timing on https://thrustcurve.org.

As you know the drag coefficient is used to determine the drag D in standard calculations (typically for incompressible flow, but this can be modified for compressible flow) using the formula :

D = Cd A (.5 * rho * V^2)

where Cd= drag coefficient
A = cross sectional area
rho= density of the fluid
V = velocity

If you know the drag, you can solve for the Cd. Typically, drag coefficients can be looked up in a reference book. The drag coefficient may be a function of the velocity or Reynolds number, but is probably pretty much a constant for incompressible flow. For compressible flow the drag coefficient may be expressed as a function of Mach number. I remember that there was a very good reference book by Hoerner on drag coefficients for many different objects (including unusual things like the Statue of Liberty), but the book is hard to find.

Both of these are amazingly helpful- thank you!

I have an old report from Estes TR-10 "Model Rocket Altitude Prediction Charts including Aerodynamic Drag" by Douglas J. Malewicki that derives analytical formulas from differential equations for finding apogee for the coast phase after motor burn-out. You would still need an estimate of the rocket velocity at burn-out (which can be done). The calculations can be done by hand, but you need to be good at math. This paper might be available from the NAR website.

https://www.rocketmime.com/rockets/rckt_eqn.html

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Is there documentation for the formulas that open rocket uses?

If I recall, there is a whole chapter in the 'Model rocketry handbook' that gives a well explained formula on "how high will it go". A great primer for a pencil & paper type calculation. You can probably also apply it to an excel spreadsheet and just enter in the variables..

Or use Openrocket or Thrustcurve like I do!

As a non-mathematician I found Randy Culp's old page (aerostadt's link in post #5) the easiest (relatively speaking) to follow. Lots of info there despite some broken links.

I have an old report from Estes TR-10 "Model Rocket Altitude Prediction Charts including Aerodynamic Drag" by Douglas J. Malewicki that derives analytical formulas from differential equations for finding apogee for the coast phase after motor burn-out. You would still need an estimate of the rocket velocity at burn-out (which can be done). The calculations can be done by hand, but you need to be good at math. This paper might be available from the NAR website.

https://www.rocketmime.com/rockets/rckt_eqn.html

Yes: Estes TR-10 or Centuri-TIR-100 Altitide Prediction Charts. Both were first issued in the early 1970's but are still available from several sources. I still have my original copies for back in the day which I use often.
Below are a couple pages from Both Centuri TIR-100 & Estes TR-10, Hope they help a little

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RASP is an old program that is very simple. It does require guessing a coefficient of drag, or reverse using it to determine Cd from an actual flight. Note it asks you the rocket diameter only, which means the Cd it uses (if you do that) is not actually Cd but Cd times a factor to include the drag of the fins. Typically a Cd of .6-.75 is used and that's fine if your rocket is very typical. If your rocket is unusual, you will need to calculate all frontal areas, convert that to an equivalent diameter, and use an actual Cd such as .35-.4 .

To Aerostar:

That's EXACTLY what I was looking for! And surprisingly little hardcore algebra, just a lot of plug-in data.

As far as everyone else:

Super helpful, all of you guys. Much more so than in other hobbies (which I won't name)!

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