Performance at less than MTOW / MTOM, and how are MTOW numbers obtained?

@Pilot_DAR hopefully will clarify. Perhaps they build a curve using different all up mass data points and then create estimates at different density altitudes? The testing is presumably quite extensive to create reliable data.

The work equation RoC = (Excess thrust HP x 33,000)/ Mass using feet/lbs is probably a crude first approximation.

It sounds like you fill the tanks up, maybe add ballast, and then adjust the performance numbers by the calculated fuel burn.

Reportedly, Socata tested the TB20 at MTOW plus 30% or something like that, and (obviously) it flew. So maybe that is the other way.

Peter wrote:

Do they add some dead weight and start the test when the aircraft is at MTOW?

Maybe they can start at MTOW*1.2, they are test pilots after all

I think performance numbers are always obtained by a combination of (a rather limited number of) semi-arbitrary measurements and interpolation/calculation. I believe others on the forum have first-hand experience. (So have I, but only in amateurish attempts which usually makes me admire the skills of the test pilots who are able to fly accurately enough to produce consistent numbers.)
Peter wrote:

Do they add some dead weight and start the test when the aircraft is at MTOW?

Would that make sense? Wouldn’t the resulting numbers only be of use to a pilot taking off overweight? Anyway, it typically would not make any difference to the performance tables or figures. For the C172 e.g. the climb to say 8000 ft would consume say 4 gallons weighing 24 lbs, which would amount to a cruise speed difference of 24/150 = 0.16 knots, using the rule of thumb from the above post. For climb performance, I agree that the numbers could arguably be considered illogical if presented for MTOM/W, but some kind of interpolation is usually applied by the pilot anyway.
Peter wrote:

how do you get the operating ceiling?

Does operating ceiling have an official definition? I think not; typically something like “100 fpm climb @ a specific weight” is used. Of course “ceiling at MTOM/W” strictly does not make sense unless provided for interpolation purposes. To my experience, very few SEP aircraft has any information about performance limited operating ceiling in the AFM (whereas many turbo’ed acft have max ceiling stated in the limitations section).

How are POH performance numbers obtained when some fuel will always get burnt off in the climb to the test location?

Do they add some dead weight and start the test when the aircraft is at MTOW?

In particular, how do you get the operating ceiling? For a typical SEP it takes perhaps an hour (flying at “best power”) to reach it.

172S POH:
During normal cruise at power settings between 55% and 75%, the true airspeed will increase approximately 1 knot for every 150 pounds below maximum gross weight.

The rate of climb is very directly affected by weight because the ROC is the conversion of surplus engine power (after drag is used up) into potential energy i.e. climbing up.

The airspeed in cruise is not much affected by weight, for typical piston GA ops which are done way beyond the Vbg (best glide speed) point and thus most of the power is used up to overcome parasitic drag, not to provide lift (induced drag, I think?). Big jets fly close to Vbg and are much more affected. If you flew a TB20 at 95kt (Vbg) instead of 140kt, you would also see a stronger weight dependence of cruise speed.

and the difference between mtow and half weight, given your average Cessna/Piper performance, is negligible (imho).

It is in my C172

Did you ever know the guy who wrote the POH is usually sharing office with the marketing guy ? sorry, stupid joke, let´s be serious – POH is for information only whatever it says in the header and what ever CAA/FAA had approved it.I used to work in the flight test department and I can assure you all the numbers are real. BUT – new aircraft, fresh engine, no insect on the propeller and wing, cabin ventilation off etc, aircraft didn´t hit the hangar wall 25 years ago and the guy didn´t tell anything to anybody. Are you sure the propeller fitted is the one used for flight test? Cruise versus climb prop makes a lot of difference. And – the guy sitting at the left seat knowing pretty well his job. Easy example – do you remember the last time you were taking off from 2 300ft grass runway (non-English grass – not a golf style) with 4 person on board in a C172/P28 ? Do you remember what the book says and how did you feel when you were the ASI was slowly approaching 52 kts ?
But back to you question – general answers, some aircraft types might be specific.
- cruise speed – weight usually do not have significant effect here. Don´t forget about negative effect of more front c.g. when the rear bench is empty.
- take-off distance – 1-2 persons on board in a 4 seater with 1/4 fuel tanks is giving you very good chance to get close to book numbers. A bit overacting here but not far from true, especially on grass runway, not speaking about wet and/or soft.
- climb rate – here you have a good chance to beat book numbers when light, climb rate is very much depending on weight.
bottom line – don´t take all the number for granted for you particular airplane, be conservative – do not expect any improvements when you left 1 of 3 guys behind.