## Calculate thrust required for a given altitude

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HattoriHanzo
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### Calculate thrust required for a given altitude

I am looking for the equation to calculating maximum thrust needed for a given altitude a rocket can fly.

If I want to fly my rocket with mass=50kg to an altitude of 5000m, how much thrust needed?
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mk
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### re: Calculate thrust required for a given altitude

You would need at least more thrust than the whole package weights. I suppose you want to lift the rocket from the ground (0 m) more or less straigth up to 5000 m.

The only question is how much fuel you will need, when stabilization and all the other problems are neglected for now.
So it's a time based question.

Assuming that the rocket delivers the same thrust from beginning to the end, acceleration is getting increased (slightly) with a rise in elevation.
Due you are moving_radially/lifting a (reducing) mass in a more or less ball-shaped gravitiy field. The equivalent work in a gravity field formula should be helpful.
So acceleration is increased by (a) reducing package mass as fuel is burned and (b) smaller gravity force "density" with an increase in elevation.
Well, 5000 m is a relatively small value when refering to the earths size, so you could always use g = 9.806 m/secÂ² instead of the integrated gravity field formula.

Then, after the motor of the rocket has shut down, the remaining rocket mass, I suppose your stated 50 kg, becomes decelerated by the (still decreasing) gravity force until it reaches the point of culmination, your requested 5000m. This deceleration time and distance depends on the achieved max. velocity.

Then only the changing mass x kg (with fuel and/or motor) -> 50 kg (without fuel and/or motor) would be a kind of major problem for a simple derivation. Hmmm...will have too look up some formulas first before I can see whether I can help you. Maybe the thoughts help you already.

But, however, your request needs to be clarified a bit more:
1. The smaller the thrust, the longer the burn time.
2. The larger the thrust, the shorter the burn time.
So it's a burn time dependened thrust question.

Of course, drag is going to play an important role, too, as speed wents up.
mk

mk
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### re: Calculate thrust required for a given altitude

Here goes an attempt. I can only try my best.

Please let me know when you find the result far from reality.
Notifying me of an obvious mistake in the presented result formula would be nice, too. Just as any correction or more correct or corrected formula.

BTW I assumed constant velocity and massflow all over the burn time.
Attachments
rocket_elevation_formula.pdf
Last edited by mk on Tue Aug 16, 2005 11:38 am, edited 1 time in total.
mk

HattoriHanzo
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### re: Calculate thrust required for a given altitude

Thank you very much! Very professional :D
I will try some calculations tomorrow, too tired right now.
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HattoriHanzo
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### re: Calculate thrust required for a given altitude

mk!

I have done some calculation and I think your formula is correct.
The problem for me right now is to figure out suitable thrust for a specific massflow.

I will come back later.
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mk
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### re: Calculate thrust required for a given altitude

Good to hear that.

However, I'm by no means a rocket (motor) expert. You may want to ask other people around to get suitable numbers or look some analysis values of certain and/or given motors up for yourself.

If you only have the complete mass with fuel (mo), just subtract the whole 1/2*m'out*tb term from the new mo value instead of adding it. This has to be done for both of the applied terms.
However, I think the adding mass methode should be the better/handier way.

Good luck.
mk

ed knesl
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### re: Calculate thrust required for a given altitude

Marten,

Unfortunately, things are lot more complicated.
Fuel used, plays a big role, also type of fuel grains.
Burning gas pressure in CC affects the thrust and burn time.
Pressure depends on mass flow and nozzle diameter and exit cone
angle and length.

There are some Excel based programs for motor and given fuel
computations.
Search web for SRM ( Solid Rocket Motor ) program.

This forum is not most sofisticated platform for rocket propulsion.

Highly recommend : Richard Nakka's Experimental Rocketry web Site.

Ed
...Nobody is right, nobody is wrong...

mk
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### re: Calculate thrust required for a given altitude

Ed,

Actually you have to apply these values in the presented formula for a certain rocket engine. It was the major problem that output velocity, massflow and burn time are affecting each other. Just as they do affect carried mass of fuel and within complete package mass. So I was and am aware of the problems.

That's why I wrote he or anybody else will have to look up suitable or correct values for a certain motor or the motor one intends to use.
mk

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### re: Calculate thrust required for a given altitude

The derivation.

Just for fun.
Attachments
Page4.jpg
Page3.jpg
Page2.jpg
Page1.jpg
mk

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### re: Calculate thrust required for a given altitude

Thanks for the hint, Ben!
mk

mk
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### re: Calculate thrust required for a given altitude

The same formula with a nicer appearance.
Attachments
rocket_elevation_formula_imp.pdf