Calculating a Booster's Acceleration?

[FrankD 7]

Hello simmers,

 

knowing the thrust in lbs provided by the booster and the weight of the thing boosted, I would like to calculate the acceleration in G, aka the "BoosterAccel" parameter.

 

Is it possible, in a simple way, for a (very much) no math guy?

 

Thanks for your attention and your valuable input.

Edited January 8, 2011 by FrankD

[Fubar512 1,350]

I use this table, once I've obtained accurate speeds and times for booster cut off, etc. http://easycalculation.com/unit-conversion/acceleration-converter.php

[FrankD 7]

Thank you Fubar, that will helps a lot.

 

As a further help, for the math/physics impaired people like me, I've found this page:

 

Force Equation Formulas Calculator - Force Mass Acceleration

 

Happy be the day wherein thou can make up for a lack of basic scientific education with a moderate skill to use Google !

Edited January 8, 2011 by FrankD

[FrankD 7]

Mmmmh, Google may not be enough to patch up for my ignorance in physics after all.

 

I thought I understood how to compute the , but I'm obtaining results that doesn't match with published figures.

 

here is how I would calculate the Booster Acceleration for an AIM-9J:

 

I know the amount of Motor Impulse, which is expressed in Lbs-sec: 8800

I know the weight of the Missile, which is expressed in Lbs: 170

I know the booster's burn time (aka "BoosterDuration" in TW's parlance), which is expressed in Seconds: 2.2

 

Now, I go on the Force Equation Formulas Calculator page, I select "acceleration" as the variable to solve and I input the Force and Mass figures, then I launch the calculation to obtain the result, expressed in m/s², as shown below:

 

 

 

 

Now, to obtain the result expressed in G, I switch to the Acceleration Unit Converter page, thanks to Fubar512, and I enter the figures expressed in "metre per second per second" with five decimals, to obtain an acceleration of 51.76471G, as below:

 

Now, I divide the Acceleration, eventually expressed in G "per second per second" by the booster's burn time, expressed in second, so 51.76471 / 2.2 = 23.5294136 or, reduced to two decimals, a BoosterAccel of 23.53 (G).

 

That is a pretty wide "near miss" compared to the 28G quoted on the "Air-to-air missile non-comparison table" or even computed by TK himself.

 

So dear knowledgeable modders amongst the wisest, where did I gone wrong in my calculation?

[Fubar512 1,350]

Nowhere in your calculations. You were simply thinking in terms of average acceleration (23.53 Gs), versus the "peak" figure of 28Gs.

 

This is why race cars and super-bikes initially outaccelerate even the newest jet fighters from a standing start, even though said aircraft may best them by the end of a quarter-mile dragstrip. Their initial peak acceleration of up to 3 Gs can only sustained for a scant few seconds (after which it may drop off to less than .5 G), while the jet's seemingly inferior .85 G peak acceleration is sustained as an average well past Mach 1.

[FrankD 7]

Thanks for your attention and your answer Fubar.

 

I thought that the "peak" acceleration was the Acceleration expressed in M/S², which is very probably a wrong assumption since, going that way, the figures would be much higher than what we have in the ini.

 

As Google led me to earthquake simulation related document that seen me lost after the first page, could you please explain, if you don't mind to probably raise even more questions, how to calculate that peak acceleration?

 

Best regards

Edited January 30, 2011 by FrankD

[Fubar512 1,350]

Thanks for your attention and your answer Fubar.

 

I thought that the "peak" acceleration was the Acceleration expressed in M/S², which is very probably a wrong assumption since, going that way, the figures would be much higher than what we have in the ini.

 

As Google led me to earthquake simulation related document that seen me lost after the first page, could you please explain, if you don't mind to probably raise even more questions, how to calculate that peak acceleration?

 

Best regards

 

There is no way to accurately calculate it, short of having precise aerodynamic, weight, and thrust data. And, there are always other factors at play, too (such as atmospheric density, attitude and initial velocity when launched, etc). The game engine is not sophisticated enough to model it to that level of fidelity, and I strongly suspect that it simply uses an average, anyway.

 

TK's the person you need to verify that last bit...

[FrankD 7]

Thanks again Fubar, I'm gonna get into my pilgrim shoes and head for the shrine.

 

May He find the question interesting enough to deserve an answer from Him.

[Fubar512 1,350]

I see that TK replied to you

 

Here's something that may help illustrate the point both of us are trying to make. Granted, both the mass and thrust involved in the example are way out there compared to what we're dealing with, but it should help hammer home why the sim uses an acceleration curve based on an average value:

 

 

Now, imagine trying write a dynamics model that allows for that level of complexity

[+Jimbib 746]

Dammit Fubar! Just when I managed to forget everything from Level 1 Dynamics from my BEng you manage to dredge it back up again

Edited January 31, 2011 by Jimbib

[FrankD 7]

Thanks for the illustration Fubar, it helps to visualize the complexity of things.

 

I was going to ask to TK about the AIM-9L's 28G of acceleration but I think that I understand his point about things being so complex in reality and "so" abstracted in the game that the figure itself doesn't really matter, it's all about the relation between the different missiles's figures and their impact on the gameplay.

 

So, what I'm going to do will simply be to rely, as much as possible, on a single source to get some kind of a consistency, even if the figures are different than the original figures or even than some of the published sources.

 

About the figures I have, the most detailed I found are from Falcon 4 as thrust values for different timing are detailed. The "fuel state" is not mentioned but the weight of the propellant is so, assuming that the consumption is linear (which is probably oversimplified), I could subtract the consumed propellant from the missile's weight and then calculate the acceleration...

 

Not sure that it will really matter though, as the results will be averaged anyway.

 

 

Edit: with this methodology, my results are very close to the figures calculated by TK! :) Of course, the arbitrary values quoted in some sources are still unexplainable, but I think that I now have a somewhat reliable way to get not so off from a probable "reality" figures.

 

Thanks again for your help Fubar512!

Edited February 1, 2011 by FrankD

[Guest HoneyFox]

Well...

 

you just convert thrust(lb) to thrust(N).

 

and now:

 

booster acceleration(g) = thrust(N) / mass(kg) / 9.81

 

the game doesn't simulate the changing mass of the missile. so there will be some small problems.

 

 

 

 

PS: welcome to try using the missile range simulator written by myself several months ago. it's in the download section.

 

though it is not very accurate (especially when missiles are having high mach speed), but the result for those subsonic and <Mach2 missiles are pretty close according to my tests.

 

now my own weapon data have perfect effects like:

 

i launch a missile at its max launch range. the enemy turn around and evade quickly and the missile finally slow down and can not chase on it. (while the missile will still be able to chase the enemy out of the range if you use the original weapon data)

 

 

Edited February 4, 2011 by HoneyFox