# How to calculate net Thrust of rocket

1. Aug 4, 2015

### deeppurple247

Trying to calculate the net thrust of a rocket taking into account the force due to gravity. So I presume this is the calculated Thrust minus the force due to gravity.

Known data so far is that the rocket gets to escape velocity (11,200 m/s) after 5 minutes (300 secs). Acceleration for this is 11,200 / 300 = 37.3 m/s/s.

Next needed to calculate the mass loss rate of fuel. Equation given for this was was q = ma / v where q is the mass loss rate, m = final mass of rocket, a = acceleration and v = fuel exit.

m was given as 50,000 kg + 2000 Kg = 52,000 kg (without fuel)

v was calculated from equation earlier with sqrt((2 * (P2 - P1))/p), with given pressures and density. This came out as 2500 m/s

So...

q = (52,000 * 37) / 2500 = 770 kg/s

From this the Thrust (T) = qv = (770 * 2500) = 1,925,000 N (It was assumed the pressures were the same so T = qv)

Calculating the total mass of the rocket on launchpad needs the weight of the fuel which I presume is the mass loss rate (770 Kg/s) multiplied by the duration of fuel (300 secs) = 231,000 Kg

Therefore the force due to gravity is...

F = ma = (231,000 + 52,000) * 9.8 = 2,773,400 N.

This is more than the thrust calculated earlier which would give a negative net thrust which cannot be correct. Can anyone see where I've gone wrong please?

Regards

2. Aug 4, 2015

### Dr. Courtney

http://arxiv.org/ftp/arxiv/papers/0903/0903.1555.pdf

The attached paper gives a method that should work. I think you will need to assume constant thrust, and used the guess and check method of integrating the differential equation until you get the given velocity at the given time, because the drag force is changing with velocity.

3. Aug 4, 2015

### deeppurple247

Thanks for quick response. One thing I forgot to mention also is that force due to drag is ignored.