# Steady-state simulation of pitching motion

Is it possible to perform a simulation of 'steady-state' pitching motion of an aircraft/wing? Is there any method where we can analyse the effects through a steady-state simulation of a pitching motion? I have seen numerous papers/articles where the unsteady simulation has been carried out but none related to steady-state.

• By definition, a pitching motion makes the process unsteady. Strictly speaking, even straight and level flight is unsteady since fuel is consumed, reducing airplane mass in the process. We assume quasi-steady conditions for straight and turning flight and even for climbs and descents, but at some point this cannot be justified any more. – Peter Kämpf Feb 16 at 7:15
• Okay! Thank you very much for the information. – angryam Feb 16 at 13:50
• Do you mean a constant rate of change of pitch, say, +3 degrees per second, maintained for more than just a few seconds? – Camille Goudeseune Feb 16 at 21:37
• In fact, constant rate of change of pitch rate (i.e. pitching acceleration is constant). – angryam Feb 20 at 17:44

A "steady" rate of pitch condition is very rare because most aircraft are designed to be stable enough to avoid stalling themselves. In other words, the more you pitch, the greater the control input you need to continue increasing AOA.

You can reach steady state in roll easily. Here drag resistance to rolling will stabilize roll rate, provided the aircraft rolls smoothly around its axis. Here, rudder and elevator inputs may be required.

So, for pitch, you could get a steady state pitch (relative to the horizon) in a loop. Here, throttle inputs are definitely required (to get a perfect circle).

But for increasing AOA at a steady rate, this will lead to a stall.

There is also the analytical consideration of acceleration before reaching steady state. Taking the easiest, the roll, roll rate goes from 0 degrees/second when ailerons are applied to steady degrees/second when drag force = rolling force (differences in AOA of rolling wings helps too).

Many early "video arcade" games do not simulate the acceleration (the deer is instantaneously in full gallop). To do an accurate simulation, acceleration to steady state must also be considered, so now you have a rate of acceleration to steady state.

• Thank you very much for such an informative answer! I understood much of what you have mentioned and I could get a feel too of what you are suggesting. However, the last paragraph seem to be little confusing and hence I am yet to comprehend it. – angryam Feb 20 at 17:46
• @angryam we start with a steady state of no motion, and end with a "steady state" of constant motion. Interesting in that "steady" can be considered in terms of distance, velocity, or acceleration. But to accurately simulate a pitching action, we must consider the acceleration to steady state velocity (with applied force). In air, it is tricky because drag opposes applied force as speed increases. – Robert DiGiovanni Feb 20 at 23:48