Simple rocket speed calculation

iioklo

I would like to get to understand rocket formulas, not being that great at maths I'll start with something simple.

If I have a rocket of 1000kg mass and its engine produces 1500kg thrust what speed would it reach in 60 seconds (it's starting from 0 speed, let's ignore gravity, drag and loss of rocket mass due to burning of fuel).

a = F/m
1.5 = 1500/1000

is this 1.5 meters per second, so in 60 seconds it will travle 90 meters, is this right.

I know speed is measured as velocity can it be determined from the mass and thrust above. Any help or alternative formulas would be apreciated.

MathsManiac

'fraid not.

The net force upwards is 1500g - 1000g = 500g newtons. In this, g is the numerical value of "acceleration due to gravity" = 9.8 approx. (By the way, when you say a thrust of 1500 kg, I'm taking this to be "kilograms force"; the SI unit of force is the newton, and you need to multiply by g to turn kilograms force into newtons.)

a = F/m = 500g/1000 = g/2 = 4.9 m/s/s.

That is, its velocity is increasing by 4.9 m/s every second. After 60 seconds, the velocity will be 4.9*60 = 294 m/s.

By the way, in practice, you couldn't ignore the mass of fuel being lost. As far as I'm aware, a high proportion of a rocket's mass is fuel, and a lot of it gets burned up in the early part of the journey.

alan4cult

It's not rocket science...



















Apologies, I just had to say it!

Capt'n Midnight

MathsManiac wrote: »

By the way, in practice, you couldn't ignore the mass of fuel being lost. As far as I'm aware, a high proportion of a rocket's mass is fuel, and a lot of it gets burned up in the early part of the journey.

http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

Only a few 3% or so of the launch mass reaches orbit, which is about the same mass as the fuel used in the first few seconds. Saturn V got 15,000Kg lighter per second.

By comparison n to get from the moon to lunar orbit you can get 50% of the original mass into orbit. In the case of the 1000Kg rocket the initial gravity drag would only be 1/6th that down here. So your rocket would have maybe 1,333Kg of thrust instead of 500Kg


equations
F=ma you know the force and the mass => acceleration
height=ut + 0.5 at^2 u=initial speed = 0 t=time a= ^^
speed is just acceleration by time

in the real world mass changes A LOT , this increases your acceleration unless you throttle back the engines , which then changes your rate of loss of mass , which changes ....
your acceleration is is limited by how many g the crew / structure can handle
the thrust from the engines also varies with air pressure being higher in a vacuum


in the real world air resistance changes , it goes up as you go faster , but goes down as the air gets thinner. Again the limit depends on how much weight you can spare for streamlining and structural support instead of fuel , and you ditch the covers as soon as you clear the atmosphere. On the Saturn V they also dropped the escape rocket very soon after launch. Air resistance can also vary according to the size of the rocket exhaust which depends on speed , thrust and altitude.




Despite all the "progress" in rocketry the Russians are still using a design from the 1950's.

iioklo

Thanks for the replys. It'll help me get to understand it a bit better.