Bf 109 G and further level flight trim, "zero" trim, dive recover forces, etc

Yo-Yo · January 24, 2018

The old discussion about "Zerotrimhandsoffflight" pops up time to time. The person who fought for the "Zerotrimhandsoffflight" on the forum(s) have sown the seeds of discredit.

The old discussion with documental proofs seems to be forgotten now, so I think, this post will have to be stuck and no comments will be allowed here not to let the post to be sunk.

This post will be an ultimate attempt to explain why 109 flies hands off just at cruise and not further.

First of all, there are two independant documents from valued test facilities: Messerschmitt AG and NII VVS (Air force research institute, USSR), both for 109G.

Both reports clearly identified the conditions of the flight tests: masses, balance, stab incidence angle, power rates. Though German report has these conditions not exactly coincided with Russian it can be used (knowing the main tendencies on CoG and stab incidence changing.

Let's start with Russian report because it covers wide ranges of CoG position at two stab positions.

The tests were conducted at 4000 m, so at the IAS of the test compressibility effects on stability can be presumed negligible.

To measure forces and controls deflection the tested plane was equipped with controls travel recorder and dynamometric flight stick. All measured experimental points were plotted at the graph as well as generalised curves. The results one can see at the graph: a full power even with full nose-heavy trim setting can not provide zero stick force. The pitching up effect of full steam propeller is very pronunced at low speeds.

At idle (gliding) zero force points is specified on the graph, so the maximal speed for hands off flight can not be higher than 390 kph (+- because of very low angle between X-axis and the curve, but the experimental points tell that minus is more plausible).

Ok, some critical minds could think, Russians had not mint-fresh plane, possible deformed, restored, etc. Or at least their NII VVS had poor instrumentation, poor test pilots and got wrong data.

Surely, it's not a good situation if you have to use only one source - any source must be checked for consistency using other sources.

The second source is for very forward CoG (21.2% MAC) and for the stab at +0.75 grad (just between 0 and 1.5), so the direct comparison to the WWS using these charts plotted together is not possible because all three main parameters are different - power, CoG and stabilisator position, though one can see from the German report that even +0.77 deg stab is not sufficient to have zero forces at cruise power setting (1.15 ata/2300 rpm) because the IAS for level flight will be higher than 335-340 kph at the graph.

Edited January 24, 2018 by NineLine

Yo-Yo · January 24, 2018

Before the third post will be written, I'd like to remember one funny story from very-very old time as Ka-50 was only in early WIP.

Now, everybody who has Mi-8 or Ka-50 DCS modules knows, that engines are controlled via a weighted sum of two controls - collective and engine control levers (throttles). As Mi-8 has a special mechanical system of bellcranks for it, Ka-50 designers used very simple way to get the same result - they placed throttles just to the collective lever.

As nobody ever seen Ka-50 face to face, I had to suggest it myself using only poor pictures, common sense and engineering mind :), so as ED delegation was at Kamov, one of the question was from me about these levers. A pilot (by the way - the test pilot!) began to laugh at them, it's impossible, it's your bad fantasy, etc, but an engineer agreed that the levers are placed exactly at the collective. The discussion was proceeeded in the hangar unveiling available Ka-50 cockpit... of course, the levers were at their right place, i.e. at the collective...

The explanation is that the pilot never looks under his elbow during the flight - just put the levers to the right notch before takeoff and return them to idle after touchdown... So, the fact that the levers travel with the collective never was noticed.

The morality of the story - the pilot only pays attention to the significant things and numbers...

Edited January 24, 2018 by NineLine

Yo-Yo · January 25, 2018

The next item is about stick forces and available g-loads at high speed. The g-load is limited by three main factors: the first is simple increasing of the stick force as the IAS increases AT MODERATE M-numbers. This increasing is proportional to IAS^2. As the g-load is proportional to the same value the stick force per 1g of g-load IS CONSTANT.

Generally, it is not "compressibility" as sometimes we can read on forums because this constant force to 1g exists only at the moderate Mach numbers.

The second factor is maximal CL decreasing with Mach number starting from very low values (0.2 - 0.3), so the plane can be trimmed at high AoA but the CL will not increase proportionally, very often - with baffeting. The reason is that at high AoA flow velocity over upper wing surface accelerates forming local critical Mach flow.

The third factor as well as the second one is typical for high altitudes. High Mach numbers due to higher TAS and lower speed of sound lead to trim issues - the plane typically becomes more stable due to neutral point rearward movement, and it becomes more nose heavy.

It requires higher elevator deflection to get the same g-load for the same IAS than it is required at low altitude. Additionally, the elevator itself requires more stick force for the same travel.

The result is significant increasing of the required force per 1 g.

Very often due to overspeed in dive at high altitude a plane goes to diving that seems unrecoverable but at lower altitude it is possible to regain control and recover.

Which factor limits controllability depends on IAS, M, thus on altitude.

Let's try to train ourself examining the Bf-109. There are several ways to get right hinge moments / stick forces depending on available data.

We will use NII VVS report that has all we need. First of all, Photo #13 contains required forces for Bf-109G at 25% MAC in comparison to other aircraft.

Using 2nd order extrapolation 12 kg per 1 cm for 540 kph and 14.8 kg per 1 cm for 600 kph are obtained.

Then we need fixed stick trim curves - Photo #5. It is possible to consider 1g trimmed IAS simply as CL for the certain elevator deflection

using the simple equation n*M*g = q*S_wing*CL --> CL = n*M*g/(q*S_wing), where q = IAS^2*1.225/2

Simply, if the plane is presumed trimmed for 1 g at 540 kph, for example, changing the elevator angle as for 1 g trimmed flight at 230 kph, we can get (540/230)^2 = 5.5 g.

By the way, speaking about pulling g's at 540 kph we will not use power-on curves regarding to 230 kph.

At power-on curves low speed/high AoA effects of the prop require additional nose-down elevator movement. So, the power-off curves are more suitable for the further calculations regarding the fact that high speed areas are almost identical.

There are two different methods we can use having the graphs from the NII VVS report - the first one uses Photo #13 and trim chart for fixed controls (elevator position).

THe result is about 16 kg of force changing (see attached picture), it does not mean that you must pull 16 kg - it just means that the difference between pushing at 1 g at 540 and pulling forces at 540 and 5.5 g is about 16 kg.

Additionally I'd like to explain how the red circle markers for 25% were estimated. Having the stab position constant we can use the fact of linear nature of the matter and use partial derivative for CoG small changes. As you see the difference between curves corresponding for X% of CoG changing you can extrapolate it further.

The second method can give absolute values for the forces - just using free controls chart. Keeping in mind that stick force for 1g at 230 kph must be multiplied to 5.5 it gives us initial push of 2.5 kg and pulling force circa 2*5.5 = 11 kg that gives about 13.5 kg of difference that is the good accordance with the first method result.