Force relationships - Let's settle it once and for all

[mhcasey]

I'm going to be honest, I still don't really understand this, and I'd rather admit it here than during my CFI checkride next week.

"Explain the relationship amongst lift, weight, thrust and drag in straight and level, climbs, descents, and slow flight configurations."

With no acceleration, the sum of all forces must be equal, but that's in regard only to directional forces, correct? As in, the sum of all forward = sum of all rearward, and upward = downward?

It's easy for me to see how the forward and rearward forces balance, but a bit trickier with climbs and descents. I think I'm looking at things the wrong way. If you speed up the airplane (add thrust), eventually the drag is going to increase and balance the new forward force (equal forward and rearward).

With a climb, though, you add lift to accelerate upwards, but how does your weight increase to balance this? Is it just a matter of some drag now being directed downward to equalize the lift and eventually stop the acceleration?

Hopefully this post has been somewhat understandable. Thanks in advance guys.

[tgrayson]

Originally Posted by mhcasey

I'm going to be honest, I still don't really understand this, and I'd rather admit it here than during my CFI checkride next week.

Smart man.

With no acceleration, the sum of all forces must be equal, but that's in regard only to directional forces, correct? As in, the sum of all forward = sum of all rearward, and upward = downward?

Forces are *always* directional. There is no such thing as a non-directional force.

but a bit trickier with climbs and descents.

Sure is.

If you speed up the airplane (add thrust), eventually the drag is going to increase and balance the new forward force (equal forward and rearward).

Yep.

With a climb, though, you add lift to accelerate upwards, but how does your weight increase to balance this?

Go back to our previous discussion. Lift isn't the cause of a *steady state* climb, it's thrust. Weight doesn't and can't increase, as you know.

Is it just a matter of some drag now being directed downward to equalize the lift and eventually stop the acceleration?

Drag cannot oppose lift, because they are perpendicular (by definition.) Weight is the only force whose direction and magnitude is constant. Lift is perpendicular to the flight path, and drag is parallel, by definition. You can consider thrust to be parallel, just like drag, if you assume the AOA is small and the thrust line is roughly aligned with the longitudinal axis.

Vector diagrams will show that lift is less than weight in both climbs and descents, with thrust opposing some of the weight in climbs, and drag opposing weight in descents.

[mhcasey]

"Weight is the only force whose direction and magnitude is constant."

Wow not sure why I hadn't figured that one out, but that solves a whole lot of riddles.

So to climb, you typically nose up, vectoring the lift backwards a bit and weight ends up "outweighing" it, but you've tilted thrust upwards as well, and this additional "up" force is what accelerates and eventually sustains the aircraft away from the center of the earth? (Of course, the "eventually sustains" occurs when the newly directed drag, still directly opposing thrust by definition, again increases to the point that the drag once again equals the thrust).

I need to get me an aerodynamics textbook that actually contains some math. I think it would be much easier to see what's going on here with a few equations and vector analysis. Any recommendations for a guy with a basic understanding of calc?

[tgrayson]

Originally Posted by mhcasey

So to climb, you typically nose up, vectoring the lift backwards a bit and weight ends up "outweighing" it, but you've tilted thrust upwards as well, and this additional "up" force is what accelerates and eventually sustains the aircraft away from the center of the earth?

Close. The problem you're running into here is that you're mixing two different situations: the "steady state" situation and the "transient" one that sets up the steady state.

Whenever you have a change of direction or velocity, you have unbalanced forces. In your example, if you just pull back on the yoke to climb, you increased your AOA at a constant airspeed, so briefly, lift > weight and this net force deflects the aircraft from its initial path. However, the airspeed quickly bleeds off and lift = weight again (or slightly less in this scenario) and forces are in balance. Once the climb is established, thrust = drag + portion of the weight along the flight path.

I need to get me an aerodynamics textbook that actually contains some math. I think it would be much easier to see what's going on here with a few equations and vector analysis. Any recommendations for a guy with a basic understanding of calc?

Ah, music to my ears. Skip Smith's "Illustrated Guide to Aerodynamics" will get you pretty far with just basic algebra. With a little bit of calc, you can upgrade to John D. Anderson's "Introduction to Flight." But I recommend the first book as an intro. He does a better job of explaining than the latter.

[surreal1221]

Thanks also tgrayson. . . just nice to see some pretty good explaning going on around these parts.

I nominate this thread be sent to the best of technical talk.

[tgrayson]

Originally Posted by surreal1221

pretty good explaning going on around these

Thank you!

[Sandesh]

Wow! that was amazing explanation. One more question, to be sure once established on a climb, lift neutralizes weight, so thrust is making the airplane climb? but doesn't drag eventually catch up to thrust to balance it?



Tgrayson again your explanations are amazing, I learn a lot here. Thank you!
Sandesh

[tgrayson]

Originally Posted by Sandesh

once established on a climb, lift neutralizes weight, so thrust is making the airplane climb? but doesn't drag eventually catch up to thrust to balance it?

Actually, it's excess thrust which adds to lift to equal weight. That's the thrust after subtracting out the drag. In truth, excess thrust only supports a very small percent of weight at normal climb angles.

The reason that an airplane remains in a climb is that there are no unbalanced forces to change that. This is an example of Newton's first law of motion: an object in motion will not change direction or velocity unless acted upon by a net force.