Calculate Rocket Launch Speed | Andrew's Problem

In summary, the conversation involved a discussion about the acceleration and velocity of a rocket. The initial question was about how to calculate the speed of a horizontally launched rocket, which was clarified by another user as being 35m/s². The conversation then delved into the equation for rocket propulsion and the variables involved, including the exhaust velocity. The discussion ended with one user giving a more detailed explanation and offering further assistance if needed.
  • #1
PhysicsAdict
3
0
Hey Guys,

I have a problem,

Say I have a rocket that has a mass about 350kg and produces 1250kg of thrust and I launch it horizontally, I know that 1250/350 gives me the acceleration in m/s2 (roughly 3.6 m/s2) but how do I then work out the speed?

Also if I where to launch the rocket vertically would I need a different equation to incorporate the force of gravity and if so how would I do that?

Thanks for your help!

Andrew
 
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  • #2
the expression of the rocket propulsion is that
Vf - Vi = Ve ln([tex]\frac{Mi}{Mf}[/tex] )

I hope it helps
 
  • #3
yea Ve is the escape velocity
 
  • #4
the_storm said:
the expression of the rocket propulsion is that
Vf - Vi = Ve ln([tex]\frac{Mi}{Mf}[/tex] )

I hope it helps

Thanks for the help but you seem to know quite a lot more about this than I do, could you please tell me what each symbol in that equation represents please.

Thanks again for your help!

Andrew
 
  • #5
PhysicsAdict said:
Say I have a rocket that has a mass about 350kg and produces 1250kg of thrust and I launch it horizontally, I know that 1250/350 gives me the acceleration in m/s2 (roughly 3.6 m/s2)
This is incorrect.

Why should it be 3.6m/s² and not, say ft/s²? Or miles/hr²? Or any other unit of acceleration?

If you take 1250kg/350kg = 3.6. There are no units. You get a unitless quantity for something that should have a unit. That should be your first warning sign.

You cannot have 1250kg of thrust. Thrust is a force, and kg are units of mass. Two entirely different quantities. What you really have is the amount of thrust equivalent to weight of 1250kg under normal Earth gravity. That's 1250kg * 9.8m/s² = 12,250N of thrust.

Now the acceleration is F/m = 12,250N/350kg = 35m/s². That's your acceleration. Note that this is roughly 3.6G, which is really what you get when you divided the two numbers above.


If the thrust and the mass of the rocket remain constant, then the final velocity is just acceleration * time. So if your rocket was running for 5s, the final velocity would be 35m/s² * 5s = 175m/s. Notice that the units still work out.

However, a real rocket produces thrust by burning fuel, so its mass will decrease. That's why you generally need to use the equation given by the_storm. In that equation,

Mi = Initial mass of the rocket.
Mf = Final mass of the rocket.
ve = Exhaust velocity. Also known as Specific Impulse.
vi-vf = Change in velocity you get between Mi and Mf states of the rocket.
ln(x) = Natural logarithm.

The problem, of course, is finding ve for your rocket. It's not always given. However, most rocket engines give total impulse. For a rocket with constant thrust, total impulse can be found by multiplying thrust by amount of time the engine runs. Then, if you take that total impulse and divide it by (Mi-Mf) you will get exactly ve. Note that if total impulse is given, this will work even if total thrust is not constant, because thrust usually varies due to the rate at which the fuel is burnt, and not due to the changes in ve.

If you are just curious, I hope that clears a few things. If you have a more specific problem in mind, you'd probably have to share some more details before we can help you better.
 
  • #6
all of what you said is correct :).
physicsadict listen to K^2.

--
Best regards
 

What is the purpose of "Calculate Rocket Launch Speed | Andrew's Problem"?

The purpose of this problem is to determine the speed at which a rocket must be launched in order to reach a specific destination.

What factors are involved in calculating the rocket launch speed?

The main factors involved in calculating the rocket launch speed include the mass of the rocket, the force of thrust, and the angle at which the rocket is launched. Other factors such as air resistance and gravity may also play a role.

How is the rocket launch speed calculated?

The rocket launch speed is calculated using the formula v = √(2 * F * sinθ / m), where v is the launch speed, F is the force of thrust, θ is the angle of launch, and m is the mass of the rocket.

Why is it important to calculate the rocket launch speed?

Calculating the rocket launch speed is important because it ensures that the rocket has enough speed and thrust to reach its intended destination. It also helps in planning and designing the rocket's trajectory and fuel consumption.

Are there any limitations to this calculation?

Yes, there are limitations to this calculation as it assumes a constant force of thrust and neglects other factors such as air resistance and gravity. Additionally, the actual launch speed may vary due to external factors such as wind and temperature.

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