# Ground run of an Aircraft Formula

1. Dec 11, 2008

### Reazar3

Hi, I am trying to work out the ground run distance of takeoff for an aircraft. I cant really write the formula down because of the length and many variations of it so im just hoping that you know what im talking about.

I am trying to work it out for a cessna 172 so i am expecting a distance around 250m for the ground run. At the moment i am getting 105m which is definately wrong compared to the existing data on 172s. Ive tried several different formulae but they all give me the same problem.

I suspect that it could be the fact that thrust is needed in the equation and the cessna is measured in hp however i converted it to force using F=P/V and used that in my calculations. Ive checked my workings countless times but i just dont know whats wrong.

I am in a bit of a hurry so if you want to know the variables and equations i can send them to you via email.

Thanks,
Alex

2. Dec 12, 2008

### turin

From the miniscule fragment of information that you have given, I suspect that this is your problem. The hp that you're using, is that at the engine, or is that delivered to the aircraft? It can be quite complicated to determine hp delivered to the aircraft is all you know is the hp produced by the engine(s). The typical aircraft propulsion is gaseous thrust, either by propeller deflecting air molecules or by hot gas exhaust. The hp of the engine may have little to do with this. If it is prop driven, then you need the speed and geometry of the propeller. (And then I guess ignore hp of engine altogether). If it is jet driven, then you need the speed and rate of exhaust gas. (And, again, I guess ignore hp of engine).

Note that the amount of runway required for take off is lower-limited by the hp of the engine (among other factors, and assuming no tail wind). So, what you've calculated, I believe, essentially amounts to a theoretical lower limit on the length of the runway if you were somehow able to harness 100% of the power produced by the engine into pushing the aircraft. I suppose that is an interesting number.

3. Dec 13, 2008

### Reazar3

Yea i know it wasnt much information but i have done like 10+ pages of calculations hence why i said if you need it id email it to you. Anyway, i have figured it out now, it was the thrust value, i ended up using an ESDU document on how to estimate thrust for light prop aircraft and the new thrust value it gave me was half of what i had before. :)

4. Dec 23, 2008

### deepthishan

post the equations youve been given please.
direct integration seems too messy esp with so many functions involved, so i think your'e using a program (matlab/fortran) right?
i did a project on a similar problem so i think i may be able to help you but i need the info given to solve it

5. Jun 10, 2011

### maarich

How do we calculate the lift coefficient during ground run and landing. Ground run and landing includes the airborne distance.