Brainteaser Question: Crosswind Landings

[Silvaire]

No, it's not that simple because it adds variable drag to the equation.

What variable drag? There's no difference in drag for an airplane flying a course of 270 degrees regardless of what direction the wind is blowing. Go ahead and pull out the old E6B and give it a whirl. Airspeed is constant, only heading and groundspeed are different. You're going to have a higher groundspeed if the wind is 180 as opposed to 270.

 

[Henning]

What variable drag? There's no difference in drag for an airplane flying a course of 270 degrees regardless of what direction the wind is blowing. Go ahead and pull out the old E6B and give it a whirl. Airspeed is constant, only heading and groundspeed are different. You're going to have a higher groundspeed if the wind is 180 as opposed to 270.

The difference between "crab and kick" and "slip down final" is what adds drag to the equation.

 

[luvflyin]

Apologies if this has been asked before, but upon cursory examination I haven't seen it here. I have my own ideas on this topic but was curious how others would chime in:

A C172/PA28-181 is doing pattern work on runway 27 with the winds steadily blowing 270 at 5kts. The pilot has been turning final in the same place, at the same speed and applying the same power/configuration settings each time resulting in a touch down on the same spot each time. After about an hour of this, the winds suddenly shift to 180@5kts just as the plane is rolling out on final.

1. If the pilot continues making the same power/configuration changes and using the same indicated airspeed but uses a crab&kick to compensate for the crosswind (i.e. the pilot makes no other compensation for the crosswind other than a crab angle in order to stay on the centerline), will the plane:
a) touch down on the same spot as before
b) touch down closer to the approach end of the runway
c) touch down farther down the runway

2. If instead of a crab&kick the pilot uses a forward slip where will the plane touch down relative to when the winds were 270 at 5kts?

3. Where will the forward slipping plane touch down relative to using the crab&kick?

I can't figure it out. You lose the headwind which would put you farther down the runway. But then there is some loss because you are "flying sideways." My guess is, in the crab and kick scenario, the loss of head wind will win out over the "flying sideways" and you'll land long longer. In the forward slip on final scenario it's up to you where you'll land. Start the slip at the right time and use the right amount of slip and you can put it on the "spot." Doing the more typical crab on final and then go into a sideslip just before touch down scenario, you should still be able to hit the spot if you time the kick and bank into the sideslip just right. I think.

 

[luvflyin]

I'm with Gwen on this interesting and theoretical question. I do wonder, however...if the plane came up short (and let's say) crashed right on a state line...which state would you bury the survivors in?

In the other state that the non survivors are buried in.. Who wants a bunch of dead people stinking up their grave.

 

[Silvaire]

The difference between "crab and kick" and "slip down final" is what adds drag to the equation.

Sorry, I thought it had been made clear that the #2 question "slip down final" was unanswerable since it negates the "continues making the same power/configuration changes" criteria. I mean it's kind of like asking "If I change my power setting will I land longer or shorter?"

I can't figure it out. You lose the headwind which would put you farther down the runway. But then there is some loss because you are "flying sideways." ...

Like I said, turn off the magenta line maker and pull out the old E6B. For any given course your slowest groundspeed will be when the wind is directly on the nose and you aren't "flying sideways" (as you put it) because course and heading are the same. When the wind is exactly 90 degrees off the course your airspeed and groundspeed will be equal and anything aft of those points your groundspeed will be higher than your airspeed.

The fact is you are never "flying sideways" it's just your ground track that's making you think you are.

 

[wishboneash]

Sorry, I thought it had been made clear that the #2 question "slip down final" was unanswerable since it negates the "continues making the same power/configuration changes" criteria. I mean it's kind of like asking "If I change my power setting will I land longer or shorter?"



Like I said, turn off the magenta line maker and pull out the old E6B. For any given course your slowest groundspeed will be when the wind is directly on the nose and you aren't "flying sideways" (as you put it) because course and heading are the same. When the wind is exactly 90 degrees off the course your airspeed and groundspeed will be equal and anything aft of those points your groundspeed will be higher than your airspeed.

The fact is you are never "flying sideways" it's just your ground track that's making you think you are.

How did you get a higher ground speed if your track is 270 and the wind is 90 deg from your left (180)? You will need to turn slightly into the wind (lets say heading 265), losing some ground speed. If you put this into a calculator and reduce your TAS to something really small, you will see the dramatic effects of the ground speed reduction. For a typical GA aircraft flying TAS=70kts, a direct 5kt x-wind will cause a negligible reduction in GS.

 

[Silvaire]

How did you get a higher ground speed if your track is 270 and the wind is 90 deg from your left (180)? ...

Higher than it would be if the wind were 270 is what I said. A 5 knot wind 90 degrees from your course will have little effect on an airplane with 100 knots of airspeed. A 50 knot wind will indeed knock 13 knots off your groundspeed. The OP's question was talking about 5 knots of wind.

 

[wishboneash]

Higher than it would be if the wind were 270 is what I said. A 5 knot wind 90 degrees from your course will have little effect on an airplane with 100 knots of airspeed. A 50 knot wind will indeed knock 13 knots off your groundspeed. The OP's question was talking about 5 knots of wind.

Darn, I have been stupid. The answer is of course (c)! The headwind component significantly reduced as wind went from 270 to 180. I was somehow thinking of going from an initial 0 headwind to a 5kt direct xwind. The difference between the slip and crab has to do with the drag difference. I am guessing the crab is less draggy than the slip.

 

[Henning]

Darn, I have been stupid. The answer is of course (c)! The headwind component significantly reduced as wind went from 270 to 180. I was somehow thinking of going from an initial 0 headwind to a 5kt direct xwind. The difference between the slip and crab has to do with the drag difference. I am guessing the crab is less draggy than the slip.

Right, but the crab doesn't introduce extra drag, it introduces extra distance because you are flying the virtual hypotenuse of a triangle crabbing whereas you fly the mid length leg of the triangle with extra drag in the slip. So the question becomes is what is the order of the extra energy consumption, the distance of the short leg of the triangle, the slip, or the difference in headwind component? The headwind vs the crab kick can be figured, but not the slip.

As was pointed out already, the variables introduced with such a minute wind component applied to a 60 knot final will be so small, the differences would be well within the margin of error of your ability to fly the exact same patterns. But this was already acknowledged in the OP making it strictly a thought experiment.

The reason it can't be calculated is because the coefficient of added drag in the slip is unknown, otherwise I'm sure the math whizzes on the board would already have a three page flame war going on.

 

[wishboneash]

Right, but the crab doesn't introduce extra drag, it introduces extra distance because you are flying the virtual hypotenuse of a triangle crabbing whereas you fly the mid length leg of the triangle with extra drag in the slip.

The reason it can't be calculated is because the coefficient of added drag in the slip is unknown, otherwise I'm sure the math whizzes on the board would already have a three page flame war going on.

I tend to agree. The crab is aerodynamically no different than normal flight. The slip configuration has a different drag coefficient and whether the difference in energy dissipated due to a longer path or a different drag value is a simulation exercise.

 

[luvflyin]

.

........otherwise I'm sure the math whizzes on the board would already have a three page flame war going on.

.
pi R 2. No, pie are round, cornbread are square.

 

[DavidWhite]

My farts move through stagnant air faster than 5 knots!

Invalid question!