Aircraft Performance Course: Turning Performance – Maximum Load Factor
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Aircraft Performance Course: Turning Performance – Maximum Load Factor

September 6, 2019


Hello! Maximum turning performance, in case we are
considering horizontal steady coordinated turns, can be expressed in the time required
to turn or the radius required to turn. As you can imagine, the bank angle plays an
important role in this. The steeper an aircraft is banked, at a specific
airspeed, the smaller the turn radius and time to turn will be. In terms of maximum turning performance, it
is therefore important first to solve the problem of the steepest turn. The steepness of a turn is defined by the
bank angle and therefore also by the load factor. So how do you determine the maximum load factor
that can be achieved? For this, the performance diagram can be used. It shows maximum thrust available and the
aerodynamic drag in symmetric flight. However, in a turn, the pilot will have to
increase the angle of attack and thereby the lift and drag coefficient. So the basic performance diagram is not valid
for turning flight. Obviously, engine performance is not affected
by the bank angle of the aircraft. The aerodynamic drag as a function of airspeed
is affected on the other hand. Let’s see how drag as a function of airspeed
change in a turn. To do this, I will highlight one point on
the drag curve. It is associated with a specific angle of
attack and therefore to a specific lift coefficient and drag coefficient. Now assume the angle of attack is kept constant. CL and CD are fixed and we determine what
happens to airspeed and drag. Let me show you how that works. So if we start with the load factor equation, load factor by definition is lift divided by and lift can be expressed as CL*0.5*rho*V^2*S. Now in the diagram we saw airspeed on the x-axis. So, lets re-write this equation and single out airspeed. If we do that, we get that the airspeed is (n*W*2/S/rho/CL)^0.5 And this is equal to the sqrt(n)*sqrt(W*2/S/rho/CL) And remember that this term is the airspeed in horizontal symmetric flight. So, this is what happens to the airspeed and now lets have a look at the aerodynamic drag. Now drag by definition is CD*0.5*rho*V^2*S and we know what airspeed is. so, its CD*0.5*rho*n*W*2/(S*rho*CL) And these terms of air density nicely cancel out. We have a half here and two (cancels out). and of course I forgot to write down S over here. So, S cancels out as well. And what we end up is following: So we see drag is (CD/CL)*n*W So in fact CD and CL are only function of angle of attack so, we kept those constants so essentially if drag increases with load factor then its proportional to the load factor. Thus, the airspeed must increase proportional
to the square root of the load factor to maintain the vertical force equilibrium in case angle
of attack is kept constant. The drag however will increase proportional
to the load factor for a fixed angle of attack. So this point is going to move upwards and
to the right. You could do this exercise for the complete
graph. As a result the whole drag curve shifts upwards
and to the right. Two interesting things can be observed. The minimum airspeed is increased. The stall limit is encountered at a higher
speed because part of the lift is used to for turning and not to balance weight. This must be solved by increasing lift by
an increase in dynamic pressure. At the same time, it is not possible anymore
to fly at certain airspeeds since the drag is more than the maximum available thrust. So, there are two factors limiting the turning
performance: the aerodynamic limit and the propulsion system. In principle my objective is to determine
the maximum load factor at each airspeed. Let’s say we calculated the performance
diagram for various load factors. You can see the different drag curves over
here. Now let’s go through the airspeed range,
starting with the lowest airspeed in horizontal flight. The stall limit is encountered at a load factor
of 1. Hence, the maximum achievable load factor
is 1. At a slightly higher airspeed, the stall limit
is encountered at n=1.5 in this example. So the maximum achievable load factor is 1.5. If we go to an even higher airspeed, the thrust
limit is encountered before the aerodynamic limit. In this case, the maximum achievable load
factor is 2. Now we can go through this complete diagram
to have all combinations of maximum load factor and airspeed. You can see there is one airspeed which give
the highest load factor for the complete airspeed range. Typically this occurs near the minimum drag
condition where the ratio of CL over CD is maximum. Concluding, the maximum achievable load factor
as a function of airspeed can be determined quickly based on the performance diagram. It essentially depends on the aerodynamic
characteristics of the aircraft, the propulsion system characteristics, and finally also two
factors which we considered constant for the moment. The air density, or altitude, and the aircraft
weight.

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