PPRuNe Forums - View Single Post - The yaw/slip thread (merged) aka Aerodynamics 101
Old 13th Sep 2004, 14:36
  #45 (permalink)  
ft
 
Join Date: Oct 2000
Location: N. Europe
Posts: 436
Likes: 0
Received 0 Likes on 0 Posts
“2. The horizontal forces on a twin engined aircraft having asymmetric thrust flying in steady straight unaccelerated level flight, wings level, can be accumulated and represented by just three distinct forces familiar to us.

[...]

2.2 Total Drag - Acts parallel to an aircaft centre line. Equals Thrust. Vertical positioning of Total Drag line irrelevant. NO relationship to weight or cg.”

In my world, drag is always parallel to the direction of travel, no matter if it is horizontal or vertical. An academic point to be sure, you’re simply splitting up what I’d call total drag into the components parallel and perpendicular to the fuselage. The summed total will, for the horizontally unaccelerated case, be parallel to the direction of travel.



That said, here’s another version of what I posted above.

To fly straight and level with thrust asymmetry, you need to push rudder into the live engine to counter the moment generated by the thrust asymmetry which will otherwise turn the aircraft towards the dead engine and make it turn flat (at best).

This opposite rudder creates a lateral force towards the dead engine at the rudder. The opposing force to this lateral force will be generated by a side slip into the dead engine and the resulting aero forces on the fuselage. With the right amount of rudder and slip for the airspeed, the moment will be the same as the moment generated by the thrust asymmetry, the forces will cancel each other out and you will be flying straight.

Rather than having this balancing force created rather inefficiently by going sideways, you can bank the aircraft and have it generated by the wings. Generating forces is what airfoils do best as that is what they are built for.

The vertical component of lift from the wings and aero forces on the stabiliser will, together with m*g applied at the CoG (remember, we’re back in the vertical plane for a moment – pun unintentional), have to cancel out summed up as a moment about an arbitrarily chosen point (which never has to be the CoG as the moment is equal about any point on a rigid body... albeit it will begin rotating about the CoG when the summed moments don’t amount to zero). They also have to cancel out with their magnitudes summed up, unless you want to accelerate vertically. This dictates the amount of vertical force on the stabiliser for any angle of bank.

The horizontal force on the stabiliser has to equal the horizontal component of lift generated by the wings. The moment generated by the fixed moment arm between them has to equal the moment generated by the thrust asymmetry. The magnitude of these forces is set by the angle of bank. Alas, the thrust asymmetry dictates the angle of bank. We have very few options. Newton still has the upper hand on us!

We could center the rudder and bank enough to increase the slip into the live engine until the aero force generated on the fuselage equals the horizontal component of the lift and the angle of attack of the fin with no rudder (camber) generates all the torque to counter the thrust asymmetry. However, generating a force through slipping is not likely to be any more efficient now than when we were wings level.

No, keep that foot on the rudder to keep the nose pointed where we’re going. That slip would be creating loads of drag and pointing the remaining of thrust to the side instead of in the direction in which we want to go, just when we lost half the thrust available to begin with and are likely to be desperate for more of it!

Besides, we banked to get away from slipping into the dead engine. It’d be rather daft to start slipping the other way instead. It’s much better to let the airfoil things at the back take care of the force generation. As was pointed out before, that’s what they’re built for. They also have a longer moment arm, meaning they'll do more torque with less drag.

This conclusion valid as long as we’re going for performance. If we are going for maximum control authority, a bit of sideslip is probably preferable. That way, we’ll leave the rudder less deflected and have more travel to use for changing our situation.

If you are hard pressed to find any disagreement with Milt here, you’re right. I’m just looking at the same thing through a different window to broaden the perspective and perhaps get some feedback.

Regards,
Fred
ft is offline