# How can I calculate takeoff distance in a generic way?

I want to build a generic performance app.

For many of the aircraft the only available method is using the takeoff charts manually (I'm not referring to the more simple-to-calc short field charts but to the charts which consider also the wind components).

Is there a way to convert these charts into numbers that allow me to calculate the output once certain parameters (weight, OAT, PA) are entered? Is this data available somewhere? Or do pilots do it with chart and pencil for every flight?

(Not a pilot myself.)

example of takeoff chart :

• If the chart is straight line i believe you can calculate the gradient and work from there. Do you have any chart on hand? Commented Nov 11, 2018 at 14:48
• I edited the original post with an example Commented Nov 11, 2018 at 14:52
• These are usually also available in tabulated data form, but not always. Usually you can convert them to data points, I had made a program quite a while ago that would load in an image then you would click to define the two axes and click on the lines to generate a chart. Commented Nov 11, 2018 at 18:33
• Welcome to aviation.SE! I just edited your question a little, but I don't completely understand what you're asking. Are you asking if it's possible to calculate takeoff distances for any aircraft based on a few generic parameters? Or are you asking how to convert a performance chart for a single, specific aircraft into a mathematical formula? Commented Nov 11, 2018 at 21:36
• Thank you ! tabular performance charts enable me to enter their data into excel (for example) and create a formula to get the results.The other chart type (one of the users commented they are sometimes called a "run-around-chart") require manual calcuation , using lines , as per the example I attached.My question is - is there a way to have these charts as tabular data as well ? since these are graphs I assume the data exist somewhere. Commented Nov 11, 2018 at 21:40

For air carrier type aircraft, the chart you show in your question (sometimes called a "run-around-chart") is generally digitized in some form (performance data printed out on dispatch release, or in a Flight Management Computer on board the aircraft or handheld device provided to crews).

For light aircraft, likely there are many software apps available for the most popular types.

Here is a picture of an Apple APP I noted online for a Cessna 172.

• Thank you for your answer.Most , if not all , apps and software refer to one model.Cessnas are especially simple as they all come in tabular chart data that one can create a formula from.I mostly refer to the other performance charts without the tabular data available. Commented Nov 11, 2018 at 21:44
• Are you specifically aiming for light aircraft? That is, aircraft with very limited performance, payload, etc.? For air carriers, many are using an app similar to the one Aircraft Performance Group (flyapg.com) makes available. It is capable of accounting for head/tailwind, runway slope, various forms of runway contamination, aircraft contamination (e.g. deice fluid), temperature, altitude, net climb, obstacle clearance, etc. Commented Nov 12, 2018 at 5:28
• Indeed I'm aiming for the General Aviation aircraft , but this should include all except commercial.Will check the site you mentioned.Thank you Commented Nov 12, 2018 at 6:05

One way would be to calculate the total energy change needed for a take-off and then to calculate how long the engine has to run to provide the aircraft with that energy. Once you have time and speed, calculation of distances should be easy. Calibrate with the charts if needed.

The total energy is the sum of mass times speed change squared divided by two, weight times elevation gained (or lost) from runway slope and weight times the height when the take-off is complete. The speed change can either be from static to lift-off speed (plus or minus wind speed) or to the multiple of stall speed required by your definition when the take-off is complete.

While at the start of the take-off sequence drag will be negligible, you need to reduce net thrust by the drag of the moving aircraft. This is generally the hardest part, but if you are willing to accept some error, a simplified drag model can be used which assumes friction and rolling drag while the aircraft accelerates, then adds induced drag as the aircraft rotates and reduces overall drag as the aircraft accelerates after take-off. Also, don't forget to model the speed dependency of thrust as well.

• My gut feeling is that while this is a very valid first principles approach, there would be too many assumptions included for it to be safely used in real operations when not based on certified or at least manufacturer-endorsed data. For example, propulsion efficiency, landing gear drag, rolling resistance are all important factors which are not normally well known outside the aircraft manufacturer except when specifically published. Not my downvote despite not agreeing :) Commented Nov 12, 2018 at 20:17
• @CptReynolds: That is why I propose to calibrate the mathematical model using existing take-off charts. I've done this myself and generated more precise data than an actual flight test because measurements in flight test have their own margin of error. In other words: I speak from experience. The downvote was by someone who simply did not understand the concept. Commented Nov 13, 2018 at 19:52
• That is a very good approach, and I agree re. flight test inaccuracies. Will supporting the model with takeoff charts allow identification of individual effects, only the combined total effect of which is in the charts (I.e. thrust and drag at low rolling speeds are both unknown, and from the chart you can identify acceleration but not individual forces)? Commented Nov 14, 2018 at 5:22
• @CptReynolds You are right, the charts only give you the sum of all forces. But there should be charts for different flap settings, wind speeds, elevations, temperatures … in other words, enough to calibrate the model for all those parameters. And the goal is to arrive at generic take-off distances. In order to determine all drag contributors, I would recommend some serious bookkeeping. Commented Nov 14, 2018 at 18:13