Computer Model of Launch

[Philosophaie]

I am trying to make a computer model of a Space Shuttle launch. Wikipedia give some data but does not give a path to follow. Any more comprehensive sites would be helpful.

Here is my math:

MN = 1e6 * kg * m / s^2 = 1e3 * kg * km / s^2

acceleration = Force(in MN) / Mass (Is this correct?)

Mass varies as fuel is consumed and parts ejected.

 

[csanders]

kg * m / (s^2 *1e6) = MN

If you had 1 kg, accelerating at 1m/s^2, it would be 1N, or .000001 MN.

But one MN = 1e6 N. So 1e6 N = MN = 1e6 * kg * m / s^2...

Now I'm confused.

I guess it depends if MN is a value, or a label.

If you're trying to find force, in Mega Newtons, divide kg*m/s^2 by 1e6.
If you're trying to find out how much force 1e6 kilograms * 1 meter per second squared is, it's 1MN.

 

[Philosophaie]

Just stating a fact on the MN conversion factor.

Need to know if acceleration equation is correct!

 

[csanders]

I think I had to much beer tonight.

MN/(1e6) = N = kg*m/s^2

So: MN = 1e6 * kg*m/s^s

I was treating kg and m like software variables (I'm a computer programmer), where kg could be 123 kilograms, and m/s^2 could be 232 m/s^2. If that was the case, and MN was another variable (representing units in mega Newtons), you would divide the result (123kg * 232m/s^2) to get the value in MN. (it's 0.028536 MN by the way)

Sorry for the confusion. I had to sit here for a while to figure out what my brain was screwing up. Stupid brain.

 

[RisingFury]

Yes, the acceleration equation is correct...

 

[Urwumpe]

Yes, but don't ignore the units.

[math]a \left [ \frac{m}{s^2} \right ] = \frac{F \left [N \equiv \frac{kg \cdot m}{s^2} \right ]}{m \left [ kg \right ]}[/math]

any SI-prefix will go with it.

[math] \frac{F \left [MN \right ]}{m \left [ kg \right ]} = a \left [ \frac{Mm}{s^2} \right ] [/math]

 

[Philosophaie]

What is the average acceleration of the Space Shuttle in its first stages from liftoff?

I get 15 km/s^2.

That seems a little high where the gravitational forces toward the Earth are mu / R^2 = 0.00981 km/s^2 at liftoff.

 

[Notebook]

Youi may find the replies in this thread usefull:

http://www.orbiter-forum.com/showthread.php?t=8115&highlight=acceleration+curve+fitting

I was trying to match a function to a graph, similar to your task. It did wander off into thrust versus altitude, but it got there in the end!

Not everyone has Mathcad, but the equations are valid abd you should be able to see what going on. You can get a trial version of it here:
http://www.adeptscience.co.uk/download/dldcat/33/0/All/Mathcad.html

People have not been impressed with Prime, I haven't tried it, I'd go for the ver.15 demo.

N.

 

[Urwumpe]

What is the average acceleration of the Space Shuttle in its first stages from liftoff?

I get 15 km/s^2.

That seems a little high where the gravitational forces toward the Earth are mu / R^2 = 0.00981 km/s^2 at liftoff.

Please use the mass in kg, not Mg or metric tons.

 

[Loru]

I'm using simple rocket calculator for simple stage design that uses only newtons and kilograms. Acceleration here is defined as "thrust to weight ratio" at begining and given in m/s which allow me to check if stage can lift off with payload from earth (I just substract 9.81 from final T/W (lift-off) result and have initial acceleration.

---------- Post added at 01:49 PM ---------- Previous post was at 01:42 PM ----------

from F=m*a equation you can calculate initial acceleration by simple conversion:

a=F/m

since newton units are defined as kilogram * meter / second^2 and mass is given in kilograms in result you have acceleration in meters/second^2

I second Urwumpe here - consistency with units is crucial to have proper results

 

[Philosophaie]

Is there any further limiting factor than:

acceleration=Force/mass

that may limit the acceleration?

 

[RisingFury]

Air drag and gravitational losses.

 

[Philosophaie]

Where can I get supersonic (above the speed of sound and in the Roll) equation for Air Drag Force?

Below .8 the speed of sound this equation works:

Fd = 1 / 2 * Cd * density * A * v ^ 2

How do I find the air drag coefficient Cd and Surface Area for subsonic?


Sorry for double posting:
http://orbiter-forum.com/showthread.php?t=27991