Someone check my equation!

[Sun]

I have come up with a rocket equation of my own: The acceleration of a rocket(in m/s) = the thrust of all the rocket engines (in kN) combined divided by the mass of the whole rocket (in tons). So, for example, if we had 1 mainsail firing at full power, that has 1500 kN. If we get that and we have a total rocket mass of 150.0 tons, then 1500 divided by 150= an acceleration rate of 10 meters per second per second.

correct me if i'm wrong.

Also, Is the equation (if it's correct) called the TWR? I don't know, I'm not that great at rocket science.

[K^2]

Yes. 1N = 1kg * 1m/s². Consequently, 1kN = 1T * 1m/s². So if you divide thrust in kN by mass in tonns, you get acceleration in m/s².

Now, TWR is a related quantity. It is thrust of the rocket divided by weight of the rocket. Weight is just mass multiplied by acceleration due to gravity, so you have the same units as thrust. (Both are a kind of force, so that makes sense.) So in your example, the weight of the rocket is 150T * 9.8m/s² = 1,470kN. Therefore, TWR is 1,500kN / 1,470kN = 1.02. You need TWR > 1 to liftoff from Kerbin, so this rocket will just barely do so. Typically, you want TWR of roughly 2 to make efficient ascent.

I also said that what you got is related. Well, if your rocket has TWR of 1, it will accelerate in vacuum at 9.8m/s². So an alternative way is to take acceleration and divide by acceleration due to gravity. TWR = 10m/s² / 9.8m/s² = 1.02. So you get the same number either way.

[PakledHostage]

I have come up with a rocket equation of my own: The acceleration of a rocket(in m/s) = the thrust of all the rocket engines (in kN) combined divided by the mass of the whole rocket (in tons).

You're using Newton's second law to calculate acceleration given mass and force. Newton's second law is often written as: force = mass * acceleration.

You've used algebra to rearrange the equation into: acceleration = force / mass. There's nothing wrong with that.

The result of your example calculation is correct because you're using the correct combination of units.

1 metric tonne is 1000 kg so your spacecraft's mass is 150000 kg.

1 kN is 1000 kg*m/s² so your spacecraft's thrust is 1500000 kg*m/s².

1500000 kg*m/s² / 150000 kg = 10 m/s² (because the kg units in the numerator and denominator cancel each other out).

Edit: Nija'd by K^2... Seems my nerd finger's just aren't quick enough... [cracks fingers] Wax on, wax off, wax on, wax off...

[Nibb31]

Thank gods for the metric system.

[The Scientific Moustache]

so now take the next step and figure out how thrust varies over time

[Banbite]

so now take the next step and figure out how thrust varies over time

Well for rockets it's more likely that the mass varies during the time, leading to some interstingly complex equations.

[SZDarkhack]

Well for rockets it's more likely that the mass varies during the time, leading to some interstingly complex equations.

Not complex at all, the thrust is given by T = u*dm/dt, where u is the exhaust velocity (and it's negative). This should be constant for a rocket in constant pressure and constant fuel flow. The *acceleration*, however, is T/m so its rate of change should be da/dt = (-T * dm/dt) / m^2 which is positive, because dm/dt is negative (the mass is decreasing). So a is increasing, and as time goes on it increases faster and faster (m^2 gets smaller). Also, you can get the Tsiolkovsky equation (i.e. delta V) by integrating the acceleration over time and changing the integration variable to mass (and as it turns out, it works for any dm/dt, i.e. fuel flow, constant or otherwise, which is why it's more general and useful).

Of course, if you want to calculate this over a trajectory in the atmosphere, things get more complicated because the thrust isn't quite constant (the exhaust velocity depends on the pressure).

In general, equations relating to rockets (in a vacuum at least) tend to be very simple, because rockets themselves are very simple engines. So don't be afraid of them

Edited July 7, 2013 by SZDarkhack