How do I calculate how high my model rocket design will go

[mandbn]

I need to know how to calculate how high my model rocket design would go accounting for air resistance and all the other types of forces it will experience in the sky. I know I could just use OpenRocket but for what I am doing, I am expected to know how to make all those calculations by hand, as well. Also, how do I calculate how quickly it will drop after the drogue is deployed then after the main parachute is deployed?

 

[PhilC]

The way I see it you have three options:
1. Use an existing simulation such as Openrocket, Rocksim, Spacecad etc
2. Write your own program
3. Calculate by hand

1 is easy and fairly accurate.

2 requires a decent understanding of the equations of motion, drag and thrust profiles if you're going to get similar accuracy to 1. You can possibly do it by using linear approximations for very small steps, though I've found that this tends to overestimate altitude. Modeling rotation of the rocket, such as weathercocking, is quite difficult. Better accuracy can be obtained by using vector and matrix maths and first/second order differential equations, but this is not for the faint hearted.

3 is a lifetime's work if you want an accurate result. The equations of motion are intractable and cannot be solved analytically.

I go for option 1 when building my own rockets because life's too short. Option 2 is interesting when when working with undergrads and grad students. I avoid option 3 - that way lies madness.

 

[Antares JS]

I need to know how to calculate how high my model rocket design would go accounting for air resistance and all the other types of forces it will experience in the sky. I know I could just use OpenRocket but for what I am doing, I am expected to know how to make all those calculations by hand, as well. Also, how do I calculate how quickly it will drop after the drogue is deployed then after the main parachute is deployed?

This might help you. https://www.apogeerockets.com/education/downloads/Newsletter320.pdf

The best way to figure out how to account for drag is to stick your rocket in a wind tunnel and measure the drag. It is almost impossible to calculate accurately.

Same thing with velocity under parachute. When my rocket propulsion class team had to figure out the descent rate of our rocket under parachute, we tossed the rocket off a known height and measured the time it took to hit the ground.

 

[Scott_650]

Here’s a great reference - all the common calculations plus links to calculators too: https://www.rocketmime.com/rockets/rckt_eqn.html

 

[rocketguy101]

another simple approximation can be found on the ThurstCurve website simulation

 

[Chuck Rogers]

For hand calculations, for subsonic model rockets, in my opinion the best method to use is the Malewicki Closed Form Equations. You can find the equations in the Estes TR-10 Technical Report on Pages 35-39. The Estes TR-10 Technical Report is available here:

TR-10.pdf (oldrocketplans.com)

The derivation of the equations is included, but you'll need to know calculus to understand the derivation.

Don't use the altitude prediction charts, just use the equations in the back of the report. But you can use the examples in the report to check your work.

Note that you will need a full function scientific calculator.

And good for your teacher in making you do it by hand.


Charles E. (Chuck) Rogers

 

[OverTheTop]

For calculating the descent rate under chute you could tow the parachute out of a car (carefully, and in a suitable location) and use something like a spring balance to measure the force. When the force equals the mass of the falling rocket note the speed of the car (allow for wind speed if you have to ). There are quite a few on-line parachute calculators available but they might not be as much fun.

 

[Cape Byron]

For calculating the descent rate under chute you could tow the parachute out of a car (carefully, and in a suitable location) and use something like a spring balance to measure the force. When the force equals the mass of the falling rocket note the speed of the car (allow for wind speed if you have to ). There are quite a few on-line parachute calculators available but they might not be as much fun.

And don't attach the parachute to the tow bar. You'll fall off trying to read the spring balance...

 

[aerostadt]

This website has some of the same formulae as Estes TR-10, but might be easier to follow:

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