What would you do? (Checkride)

[Fly4Fun!]

I have my commercial checkride next week. I have been studying my butt off... I finally feel up to the ACS standards on both the ground and flight portion.

However, I have an issue:

The aircraft I am taking my checkride in is an old Piper Arrow. The AFM only offers one chart for takeoff performance, which is max gross. With a 1.5 margin, at max gross, with temperatures that are most likely for an august afternoon, I am not safely clearing a 50 foot obstacles.

With all that said, the situation I have been provided by my DPE doesn't have us departing at max gross. On top of that, I do not nearly need full tanks.

I know about the 30/70 rule for obstacles, and the 50/70 rule for takeoffs without an obstacle, but those are rules of thumbs to back up know performance numbers.

I believe that the correct answer is that in the interest of safety, only the know performance numbers can be utilized, and that a departure with the given conditions (HOT) is unsafe. Departing bellow max gross will have a resultant increase in performance, however how much of an increase is a guess, which is (in my opinion) an unacceptable level of risk.

Am I looking at this wrong?

 

[PeterNSteinmetz]

Sure, beyond the FAA learning. You know the takeoff distance and rotation speed for full gross. Based on that, you can determine the time it took to get to that speed. With that information you can determine the average acceleration for the take off run. With that information you can determine the force being applied over the take off run. Now you can plug your less than gross weight number back into the formulas used to determine that. You now have a new acceleration number. But it gets slightly better. Your V speeds also decreases based on the square root of the ratio of current weight to gross weight. So you can also calculate your new rotation speed. Coupled with the new acceleration rate, you can calculate the new take off distance. You can also determine with the new Vx based on current weight the horizontal distance needed to clear the 50' object.

Is it a lot of work? Yeah, maybe, but it shows to the DPE that you actually put some thought into the process.

Can also use the Koch chart.

 

[PeterNSteinmetz]

Problem with a Koch chart is that it doesn’t have a way to account for reduced (or increased) weight, so you’ve actually got to do a takeoff at the weight in question and determine your takeoff distance under some known pressure altitude and temperature combination that you can use as a baseline.

The problem with THAT is you don’t end up with the distance that the manufacturer would come up with, and so applying some percentage as a safety factor would have a basis in reality, and would actually be a “safety” factor, not just a baseless number that makes you FEEL safe.

Agreed the Koch chart will not handle weight variation. One solution is to interpolate between values if given for different weights in the tables.

If not available, it turns out that takeoff distance is treated in chapter 6 of Anderson’s “Introduction to Flight”. Equation 6.94 in edition 3 gives the takeoff run required as proportional to W^2.

So I think the OP would be on a rather good foundation adjusting by that factor. As noted in some of the discussion above, there are a number of issues which factor into this calculation from physical principles and simplifications to be made. Anderson deals with these.

It is a nice book for this sort of thing which allows one to either look up and qualitatively understand these results or dig into it at a college sophomore engineering level.

 

[PeterNSteinmetz]

But you still end up with the same placebo safety factor.

All of these things are fairly rough calculations, right? Even the measured values in the tables are fairly rough for 50 year old planes.

Personally, I would be comfortable with this correction factor from the POH tables.

But if I have less than 150% of the predicted takeoff distance available in runway length, I always figure the abort point on the runway and abort if I am not off the ground by then. I would not just blithely go beyond that point assuming I will be ok because this calculation said it should work. Plenty of time to taxi back and think some more about it.

 

[PeterNSteinmetz]

If you use your actual takeoff data, it comes out pretty close.

My 69 Cardinal has been surprisingly on the book for performance, though I have heard of others that are not. I recently had the leading edges of wing repainted because there was a lot of rough paint from a bad repair and a top overall and am now about 6 mph better in cruise! Glad I got something concrete to show for the 6 AMU top overhaul.