Relative Wind
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Relative Wind
I have a very mathematically minded student in my instrument ground school who wants a more mathematical answer to why we gain performance when the wind shears from a tailwind to either a headwind or calm wind on an approach. He thinks that there shouldn't be a performance difference because relative wind only has to do with the movement of the airplane through the air. I think he is confused about what relative wind really is. In a nutshell all general aviation books I have looked at just say relative wind is caused by the movement of the aircraft through the airmass and is opposite to the flight path. However, relative wind has vectors, correct? Relative Wind is the resultant of two components and not just caused by our forward motion. Relative Wind is somewhere between two components: one is the "natural wind" which acts in the direction the air mass is traveling (headwind or tailwind) and the other is induced by the movement of the airplane through the airmass and acts parallel to the direction of movement. You can see then that Relative Wind would be a different figure if the airmass was moving in the same direction as us (tailwind) as opposed to an airmass that was moving in the opposite direction as us (headwind). Any thoughts? Thanks!
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Relative wind in sailing boats is computed from the direction of the wind and the heading of the boat,and it changes with boat speed,but here the aerofoil is the sail ,and it is vertical.
I've not heard of it being used in aero navigation,but normally just to lay off the wind as leeway,headwind or tailwind.
Sorry if that is not much help,I'm sure you will get more informed replies.
Lister
I've not heard of it being used in aero navigation,but normally just to lay off the wind as leeway,headwind or tailwind.
Sorry if that is not much help,I'm sure you will get more informed replies.
Lister
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Relative Wind
Thanks for trying. I need more of a mathematical answer. He understands that if on an approach the wind shears from a tailwind to a headwind, then we will have an increase in performance. We will ballon up and our indicated airspeed may increase; and therefore, we reduce power and pitch down to recapture our glide slope. He is thinking that we will have the same amount of relative wind whether we have a headwind or a tailwind so our performance shouldn't be affected. However, from experience I know that our performance is affected. He is thinking that we should be making the same amount of lift on approach whether we have a headwind or a tailwind because he says relative wind is only due to the movement of the aircraft through the airmass. I can't find a FAA explanation in black and white.
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I think you will actually find this is actually due to momentum, as the wind changes from a tailwind the aircraft will initially keep the speed over the ground that it had due to momentum, thus giving an increase in relative headwind and airspeed and the resultant balloon.
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Relative Wind and Performance
Hmm... yes I see what you are saying. Well let me play devil's advocate. Let's get rid of the windshear on approach scenario. Say we are flying at cruise with a tailwind and we do a 180 degree turn into the wind. When we are flying into the wind we will get better performance (better climb, etc.) We will cover less ground in a given amount of time but our performance is better. More wind coming over our wings and over our propeller. We will have to adjust our power and pitch to maintain altitude and airspeed.
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Not really following you on the cruise scenario. The only way you will get more airflow over the wings is if you increase your airspeed. You won't get anymore air over the wings with a headwind than if you do with a tailwind.
The climb performance is not improved. Headwind/tailwind has nothing to do with RoC, but does affect climb gradient (if you have a headwind you will cover less distance in the time it takes to climb to a given altitude).
Power + Attitude = Performance
In the windsheer case the aircraft has inertia. When acted upon by a gust of wind, the change in groundspeed is not immediate, the aircraft carries on at the same ground speed as it did before. Therefore the change in wind speed has a direct effect on the airspeed of the aircraft. Sudden tailwind, Reduction in airspeed - reduction in lift; sudden headwind, increase in airspeed - increase in lift.
The climb performance is not improved. Headwind/tailwind has nothing to do with RoC, but does affect climb gradient (if you have a headwind you will cover less distance in the time it takes to climb to a given altitude).
Power + Attitude = Performance
In the windsheer case the aircraft has inertia. When acted upon by a gust of wind, the change in groundspeed is not immediate, the aircraft carries on at the same ground speed as it did before. Therefore the change in wind speed has a direct effect on the airspeed of the aircraft. Sudden tailwind, Reduction in airspeed - reduction in lift; sudden headwind, increase in airspeed - increase in lift.
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Yep agree, this "turn into wind in the cruise" has been discussed many times - try it and watch the instruments - no change of performance on wind direction change, gradient is affected but is is only apparant if looking at the effect on path over the ground (same climb rate, lower groundspeed = better gradient). A steady heading with changing wind effects the actual performance for the reasons stated.
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per drumpoet:
No, performance relative to the air mass remains the same (airspeed, ROC, ...). And that's the performance we all count on, as quoted in the POH.
But since the air mass is moving over the ground, you cover fewer miles per minute in a headwind. And thus if you climb 800 fpm, but do it over fewer miles, then your climb gradient is increased.
When we are flying into the wind we will get better performance (better climb, etc.)
But since the air mass is moving over the ground, you cover fewer miles per minute in a headwind. And thus if you climb 800 fpm, but do it over fewer miles, then your climb gradient is increased.
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Explanations of "performance" seem to be all over the map here.
From an airfoil (wing) perspective, shearing from a tailwind to a headwind creates more lift (assuming density remains the same). Lift = Coefficient of lift*1/2*p*s*Vsquared. In a simplistic world, the V factor has been changed from airflow generated by forward movement minus tailwind, to airflow generated by forward movement PLUS headwind. Additional lift generated proportional to the square of the difference.
From an airfoil (wing) perspective, shearing from a tailwind to a headwind creates more lift (assuming density remains the same). Lift = Coefficient of lift*1/2*p*s*Vsquared. In a simplistic world, the V factor has been changed from airflow generated by forward movement minus tailwind, to airflow generated by forward movement PLUS headwind. Additional lift generated proportional to the square of the difference.
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In a simplistic world, the V factor has been changed from airflow generated by forward movement minus tailwind, to airflow generated by forward movement PLUS headwind. Additional lift generated proportional to the square of the difference.
Drum poet, I think part of the confusion is in the definition of performance.
The performance of the airplane does not change with a change of wind.
The performance of the airplane is determined by engine power, density altitude,propeller efficiency etc etc etc.
The performance of the airplane is measured in forward speed and rate of climb.
These numbers don't change with a change in wind direction.
The performance of the aircraft relative to the ground does change with a change in wind direction, such as ground speed and angle of climb or angle of descent.
I think we need to stay away from airflow over the wing as it not as relevant here.
The airplane still flies, even with a 90 degr. crosswind as the wind determines the direction of the airmass and not the airflow over the wing.
So the "performance change" is really a change in direction of motion of the airmass which requires a change in the airplane performance in order to maintain the same "performance" relative to the ground; which is what we really want, maintain the same descent angle.
Let's assume a ILS approach at 90 kts.
No wind rate of descent for a 3 degree descent angle is -450fpm
With a 30 kts tailwind the GS= 120 kts, rate of descent required is -600fpm
With a 30 kts headwind the GS= 60 kts, rate of descent required is -300fpm
So if a 30 kts tailwind shears to a 30 kts crosswind and continues to shear to a 30 kts headwind we have to change the performance of the airplane to maintain a constant performance relative to the ground.
Change the rate of descent from -600 fpm to -450 to -300fpm.
Does this help at all?
The performance of the airplane does not change with a change of wind.
The performance of the airplane is determined by engine power, density altitude,propeller efficiency etc etc etc.
The performance of the airplane is measured in forward speed and rate of climb.
These numbers don't change with a change in wind direction.
The performance of the aircraft relative to the ground does change with a change in wind direction, such as ground speed and angle of climb or angle of descent.
I think we need to stay away from airflow over the wing as it not as relevant here.
The airplane still flies, even with a 90 degr. crosswind as the wind determines the direction of the airmass and not the airflow over the wing.
So the "performance change" is really a change in direction of motion of the airmass which requires a change in the airplane performance in order to maintain the same "performance" relative to the ground; which is what we really want, maintain the same descent angle.
Let's assume a ILS approach at 90 kts.
No wind rate of descent for a 3 degree descent angle is -450fpm
With a 30 kts tailwind the GS= 120 kts, rate of descent required is -600fpm
With a 30 kts headwind the GS= 60 kts, rate of descent required is -300fpm
So if a 30 kts tailwind shears to a 30 kts crosswind and continues to shear to a 30 kts headwind we have to change the performance of the airplane to maintain a constant performance relative to the ground.
Change the rate of descent from -600 fpm to -450 to -300fpm.
Does this help at all?
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the aircraft will settle down to its origional "V" in the new mass of air and resume the performance it started with.
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I didn't see any reference to assume any stability
unless the wind continues to change
)
Return to some basics and the answer becomes clear.
In UNACCELERATED flight, Lift (L) = Weight(W) and thrust(T) = Drag(D)
L= CL*1/2RHO*V^2
D=CL*1/2RHO*V^2
Now introduce a sudden increase in airspeed (V). This could be an increasing headwind, reducing tailwind or tail-headwind. It's all the same from the frame of reference of the aircraft.
Both lift and drag increase. Lift is now greater than weight,there is a net force vertically,and the aircraft will accelerate vertically. This will be felt as an increase in Load Factor (G) and the aircraft will either climb or descend at a lower rate, depending on what it was doing before the introduction of the wind-change. If the pilot combats this by lowering the nose, the speed will (momentarily) increase further.
BUT drag will ALSO increase. THIS will cause an acceleration (there is no such term in Physics as Deceleration) because Drag is now greater than thrust, so there is a net force in the direction of the tail. The airspeed will reduce (the rate of change depending on the size of the net force) until drag=thrust again. We will therefore return to our original airspeed, lift will return to it's original value (equal to weight) and we will all get on with our lives!!.
So, point out to your student that the aircraft does not instantaneously change it's ground speed to return to it's original airspeed (and the occupants would end up as strawberry jam if it did) but rather accelerates back to a state of equilibrium.
Hope that helps-next time stick this sort of thing on Tech talk, with LOVE it there!!
In UNACCELERATED flight, Lift (L) = Weight(W) and thrust(T) = Drag(D)
L= CL*1/2RHO*V^2
D=CL*1/2RHO*V^2
Now introduce a sudden increase in airspeed (V). This could be an increasing headwind, reducing tailwind or tail-headwind. It's all the same from the frame of reference of the aircraft.
Both lift and drag increase. Lift is now greater than weight,there is a net force vertically,and the aircraft will accelerate vertically. This will be felt as an increase in Load Factor (G) and the aircraft will either climb or descend at a lower rate, depending on what it was doing before the introduction of the wind-change. If the pilot combats this by lowering the nose, the speed will (momentarily) increase further.
BUT drag will ALSO increase. THIS will cause an acceleration (there is no such term in Physics as Deceleration) because Drag is now greater than thrust, so there is a net force in the direction of the tail. The airspeed will reduce (the rate of change depending on the size of the net force) until drag=thrust again. We will therefore return to our original airspeed, lift will return to it's original value (equal to weight) and we will all get on with our lives!!.
So, point out to your student that the aircraft does not instantaneously change it's ground speed to return to it's original airspeed (and the occupants would end up as strawberry jam if it did) but rather accelerates back to a state of equilibrium.
Hope that helps-next time stick this sort of thing on Tech talk, with LOVE it there!!
If there's a sudden increase in headwind, you get an increase in lift and drag. The drag reduces the airspeed to equilibrium and the performance increase disappears. The opposite happens when there's a loss of headwind - lift and drag both decrease, the aeroplane sinks, accelerates and finds equilibrium again.
A light aircraft has very little momentum and equilibrium is rapidly restored. This is why you can fly an approach in a Cessna 152 in gusty conditions with no real difficulty, though it will be a bit 'sporting'. In a larger aeroplane, large thrust changes can be needed to prevent airspeed increases and ballooning followed by airspeed decreases and sink. In gusty conditions I'd rather be in a Cessna than a 737.
A light aircraft has very little momentum and equilibrium is rapidly restored. This is why you can fly an approach in a Cessna 152 in gusty conditions with no real difficulty, though it will be a bit 'sporting'. In a larger aeroplane, large thrust changes can be needed to prevent airspeed increases and ballooning followed by airspeed decreases and sink. In gusty conditions I'd rather be in a Cessna than a 737.
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Equilibrium and Stability
If there's a sudden increase in headwind, you get an increase in lift and drag. The drag reduces the airspeed to equilibrium and the performance increase disappears.
Ignoring increases in form and parasite drag from, for the sake of simplicity, the increase in induced drag balances out the the increase in lift only when the airfoil's coeffcient of drag and coefficient of lift are equal.
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The Magic Portion
TMc,
Agreed on the definition of equilibrium. Disagree that a return to equilibrium from a change in relative wind on an approach is something that happens without additional design features or pilot input.
Agreed on the definition of equilibrium. Disagree that a return to equilibrium from a change in relative wind on an approach is something that happens without additional design features or pilot input.
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Disagree that a return to equilibrium from a change in relative wind on an approach is something that happens without additional design features or pilot input.
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Should an aircraft be affected whilst flying an approach (at an airspeed above Vmd) which results in a reduced airspeed -i.e a sudden tailwind- the aircraft will have a reudced airspeed. The reduction in airspeed will result in a loss of lift and a reduction of drag. With reduced total drag and no change in thrust the airspeed returns to that orignally flown by the pilot and equilibrium is restored. No restoring force or design features are required.
Below Vmd, drag in the same situation and the reduction in airspeed will result in an increase in total drag. Further reduction in airspeed result in an further increases in drag. Only then, is pilot intervention required.
Below Vmd, drag in the same situation and the reduction in airspeed will result in an increase in total drag. Further reduction in airspeed result in an further increases in drag. Only then, is pilot intervention required.