Help with getting an equation from a data table

[ehizzlefosho]

Hello All,

I am making an aircraft performance calculator as a fun project for myself ( I am a student pilot ). I would like to make a formula for a given pressure alt and temperature based on the distances given from the aircraft performance charts. for example pressure alt is 1643 ft and the temp is 73 F have it give me a take-off distance based on the information from the data table.

I tried doing a 2nd order poly equation but realized that the equation works for only 1 specific alt or specific temp and I need an equation that can do both at the same time.

Thanks!

Data Table.PNG

[oeldere]

Can you also add the expected result?

[MrShorty]

I'm not a pilot or anything similar, so take this as an interesting math exercise. This looks similar to this discussion: https://www.excelforum.com/excel-pro...ml#post5173967 where I observed that a relatively simple power trendline [ln(TOD)=m*ln(V)+b] seems to work well as a regression equation for take off distance. The OP in the other thread was also including load weight (m) in his TOD tables, and I also made similar observations regarding how that variable seems to fit into the same model. See what you think.

[ehizzlefosho]

Can you also add the expected result?

That is what I am trying to find. The table shows what take-off distance you can expect at a given temp and air density, and this info is directly from the aircraft manual. I am trying to turn this information into a formula to basically fill the gaps, for example, it shows that I can expect 1280ft for pressure alt @ 1000ft and 32F but I need to develop an equation to say what would my take-off distance be if I am at 1486ft and 67F.

[ehizzlefosho]

I'm not a pilot or anything similar, so take this as an interesting math exercise. This looks similar to this discussion: https://www.excelforum.com/excel-pro...ml#post5173967 where I observed that a relatively simple power trendline [ln(TOD)=m*ln(V)+b] seems to work well as a regression equation for take off distance. The OP in the other thread was also including load weight (m) in his TOD tables, and I also made similar observations regarding how that variable seems to fit into the same model. See what you think.

Wow, very similar, basically the practical application to what the OP is working on. I also have charts with corresponding weights, which was going to be the next step after I figure this part of the solution out. What is V in your equation, molar volume? I haven't used LINEST for anything this complicated, just for polynomials, how would you set up your LINEST function to fit your ln(TOD)=m*ln(V)+b equation. I would guess that you would use EXP(m*ln(V)+b) to get your final take-off distance answer?

[MrShorty]

What is V in your equation, molar volume?

Yes.

how would you set up your LINEST function to fit your ln(TOD)=m*ln(V)+b equation

Something like =LINEST(LN(known_TOD),LN(known_V)) should work.

I would guess that you would use EXP(m*ln(V)+b) to get your final take-off distance answer?

or the algebraically equivalent =EXP(b)*V^m or other equivalent expression.

[ehizzlefosho]

Yes.
Something like =LINEST(LN(known_TOD),LN(known_V)) should work.
or the algebraically equivalent =EXP(b)*V^m or other equivalent expression.

I must have something incorrect. Thanks again MrShorty!

[MrShorty]

LINEST() is an array function that outputs 2 (or more) values. As is, you are only outputting the m value (not mass but slope in the y=mx+b regression equation) and not outputting the b value. Try these edits:

1) Select X5:Y5 and re-enter the LINEST() function. X5 should contain m (slope) and Y5 should contain b.
2) Change X7 to be =Y5
3) Edit X6 so the exponent is referring to X5 =EXP(X7)*X8^X5

That should give you a better value in X6 (I get 358.483).