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Old Aug 4th 2015, 07:28 AM   #1
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Calculating net thrust of rocket with gravity

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
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
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Old Aug 4th 2015, 09:32 AM   #2
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I think there is a problem with this:

Originally Posted by deeppurple247
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
The value for a can't possibly be the acceleration of the rocket. Consider a rocket that is merely hovering, so that a=0: this formula would indicate it requires no fuel to do so, which clearly is not right. I'm thinking the value for a ought to have something to do with the acceleration of the exhaust gasses, not the acceleration of the rocket. Or perhaps the term "ma" should actually be F_thrust (perhaps in a previous calculation it is assumed that F_thrust = ma?). Can you show us where you got the equation q=mv/a?
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Old Aug 4th 2015, 10:54 AM   #3
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I note that you seem to be assuming a constant acceleration.
Since the mass is changing (as you burn fuel) but your thrust is constant, the acceleration must be changing.
This implies that your initial value for q is wrong.
This is the value of q to accelerate the empty rocket at 37m/s/s not the full rocket.
The initial acceleration will be zero, and will rise linearly as the fuel is burned.
So to get to the escape velocity the average acceleration will be 37.3, the final acceleration will be higher.
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Old Aug 4th 2015, 03:32 PM   #4
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I've played around with this a bit and I can't get it to work with the exit velocity you quote.
My calculations suggest it would require an exit velocity of just over 3300 m/s.

It's quite possible I've made a mistake, but I think there is a problem with your original numbers.
Perhaps someone else out there will point out what we are missing, but I can't see it.
Please let us know if you have a eureka moment.

ps
What are P1 and P2 in your equation for v, I guess p is indicating rho (for density)?
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Old Aug 5th 2015, 12:37 AM   #5
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MBW you're correct. The exit velocity is actually 3535.65 m/s, and yes p was ro for density. However this still means the force of thrust required (T = qv) is less than the force due to gravity.

q now equals (52000 * 37) / 3535.65 = 544.2 Kg/s (From q = (m * a) / v)

FYI the equation in the back of the booklet definitely says these values are:

m = mass of the rocket
a = acceleration of rocket
q = fuel mass ejection rate
v = fuel exit velocity

And so T = 3535.65 * 554.2 = 1,959,440 N

One thing that may be wrong is the initial calculation of the acceleration for the escape velocity. The question said...

Calculate the acceleration required by the rocket to reach the escape velocity (11,200 m/s) within 5 minutes (300 seconds). There is no other information given at this point.

So I presume it's assuming a constant acceleration of 37.3 m/s/s ?

Regards
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Old Aug 5th 2015, 05:50 AM   #6
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The problem is here: the equation q= ma/v is incorrect. The actual equation to use is T = F_thrust = qv, which gives q=T/v. It seems someone then set T = ma, to get q=ma/v. But the proper equation is sum of forces = ma, so that:

Sum of forces = T - mg = ma --> qv-mg = ma --->

q= m(a-g)/v

Try this and see if it doesn't work out better for you.
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Old Aug 5th 2015, 08:35 AM   #7
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Velocity of the Rocket : V = at
Acceleration of Rocket : a = M/T -g
T is the Thrust
g is the acceleration due to gravity.
Total Mass of Rocket : M = m + f
m is empty mass of rocket
f is mass of fuel
Mass of Fuel : f = F - qt
F is initial mass of fuel
q is the fuel mass ejection rate.
Thus
Velocity of the Rocket : V = [(m+F-qt)/T -g]t
Thrust : T = qv
v is the fuel exit velocity.
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Last edited by MBW; Aug 5th 2015 at 04:06 PM.
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