speedracer1407
Topic Author
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Joined: Fri Dec 24, 2004 4:19 pm

### Crab Angle Vs Crosswind Direction And Speed

There have been many crosswind landing questions on this forum recently, so I'm not asking for yet another explaination of how such a landing is performed.

Rather, I'm wondering what the relationship between crosswind direction and crab angle is. It's my understanding that a plane "naturally" crabs to the direction of a headwind that's offset from the runway heading. Yet, a 45 degree crosswind certainly doesn't cause a 45 degree crab angle, and a 90 degree crosswind doesn't cause a 90 degree crab angle.

Is there a calculation that determines crab angle from the speed and direction of a crosswind? Is the crab angle dependent on an aircraft's shape and size? Is it dependent on crosswind speed more than direction for vice versa?

Also, do airliners crab in a 90 degree crosswind?

Thanks for any replies,

O
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futurecaptain
Posts: 1918
Joined: Sat Sep 09, 2006 1:54 am

### RE: Crab Angle Vs Crosswind Direction And Speed

The crab angle of an aircraft varies depending on the speed of the aircraft and the speed of the wind. A faster jet will crab into the same wind less than a slower Cessna. Also a faster wind speed requires a greater crab angle.
I can get you some actual numbers in the morning, its late here. An E6-B will calculate crab angles as will a modern GPS unit in the aircraft.
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rwessel
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### RE: Crab Angle Vs Crosswind Direction And Speed

You can break a wind into headwind and crosswind components. Let's say you have a 20kt wind from 30 degrees off your flight path (IOW, about 2:00 O’clock). This appears to the aircraft as a headwind of 20kts*cos(30) (about 17kts) and a (direct, 90 degree) crosswind of 20kts*sin(30) (about 10kts). Note: all trigonometry in degrees, if you’re trying this at home, be sure your calculator isn’t defaulting to radians.

So let's say you're flying a 100kt approach. To stay on the correct ground path, you'll be flying not straight ahead, but at a point 83nm (100-17) ahead, and 10nm to the right (since that's the correction for where the wind will blow you as you fly 100nm). That heading is arctan(10/83) (about 7 degrees) off your desired ground track.

So the crab angle depends on the crosswind's direction and speed (as either increases*, the amount of required crab angle increase), plus the aircraft's speed (as that increases, the required crab angle decreases).

*ignoring a direct headwind, which requires no crab at any speed, of course.

zeke
Posts: 11662
Joined: Thu Dec 14, 2006 1:42 pm

### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting Speedracer1407 (Thread starter):Is there a calculation that determines crab angle from the speed and direction of a crosswind?

The angle is the inverse sine of (crosswind/aircraft speed) or arcsin(xwind/tas)

 Quoting Speedracer1407 (Thread starter):Is the crab angle dependent on an aircraft's shape and size?

No, it simple vector maths.

 Quoting Speedracer1407 (Thread starter):Is it dependent on crosswind speed more than direction for vice versa?

The aircraft needs to point into wind enough for the components of its speed in the direction of the crosswind to be equal to the crosswind.

 Quoting Speedracer1407 (Thread starter):Also, do airliners crab in a 90 degree crosswind?

Yes
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CosmicCruiser
Posts: 2132
Joined: Tue Feb 22, 2005 3:01 am

### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting Speedracer1407 (Thread starter):It's my understanding that a plane "naturally" crabs to the direction of a headwind that's offset from the runway heading.

If you mean the jet does it "by it's self" (natrually) no you must turn the jet and fly the crab. On newer jets you can see the drift vector on the N.D, but in older ones you just "eyeball it". no problem.

I remember a trip in the old 727 into JFK one night with the surface wind in excess of 45 degrees (maybe closer to 60 or 70 deg) at 67 kts. and because we were bouncing around so much I don't recall the crab angle but I can say we were looking at the runway thru the DV window!! There was no real way to ever get the jet on the ground. After 3 attempts we diverted to Baltimore and came back a few hrs. later with a 40 kt wind. I found out about 4 yrs. later that this was the backside of the "perfect storm" moving up the east coast. I can still see it.

FredT
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Joined: Thu Feb 07, 2002 9:51 pm

### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting CosmicCruiser (Reply 4):If you mean the jet does it "by it's self" (natrually) no you must turn the jet and fly the crab. On newer jets you can see the drift vector on the N.D, but in older ones you just "eyeball it". no problem.

Except on takeoff where they will in fact crab more or less automagically once you center the rudder and ailerons. What effectively happens is you take off in a slip and then release the crossed controls - and the aircraft points itself into the relative wing.
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vikkyvik
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### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting FredT (Reply 5):Except on takeoff where they will in fact crab more or less automagically once you center the rudder and ailerons. What effectively happens is you take off in a slip and then release the crossed controls - and the aircraft points itself into the relative wing.

Why could this not happen on landing as well? If the rudder were centered that is....

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CosmicCruiser
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Joined: Tue Feb 22, 2005 3:01 am

### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting FredT (Reply 5):Except on takeoff where they will in fact crab more or less automagically once you center the rudder and ailerons

No way. The a/c will not "weather vane" into the wind once off the grd. Let's say you can release the "cross controls" perfectly as the jet lifts off; then you'll be on the runway heading wings level and drifting downwind. Usually no one is that perfect and the jet may need a small correction to "fly runway heading".

FredT
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Joined: Thu Feb 07, 2002 9:51 pm

### RE: Crab Angle Vs Crosswind Direction And Speed

An aircraft will weather wane, i e try to point itself into the direction of flight relative to the surrounding air mass if left to it's own.

An aircraft travelling in the runway heading, as it will be on take off, will not be pointed in the direction of flight relative to the surrounding air mass.

 Quoting CosmicCruiser (Reply 7):Let's say you can release the "cross controls" perfectly as the jet lifts off; then you'll be on the runway heading wings level and drifting downwind.

At an instant just prior to liftoff, the aircraft will be travelling in the runway heading.

Agree or disagree?

At the instant just after liftoff, will the aircraft still be travelling in the runway heading?

Agree or disagree?

If you disagree, please explain how the aircraft will instantly accelerate laterally at the moment when the tires leave the tarmac.

In real life, most pilots will hold the controls crossed for a few after liftoff, thus allowing the aircraft to accelerate slightly downwind. Thus, weather waning will not suffice to put the aircraft on the runway track if that is what is desired.

 Quoting Vikkyvik (Reply 6):Why could this not happen on landing as well? If the rudder were centered that is....

If you are applying the wing low, crossed controls method of remaining aligned with the runway while not crabbing, it will indeed happen on landing as well. I can't really see any situation where this would be useful or desirable though!

Rgds,
/Fred
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futurecaptain
Posts: 1918
Joined: Sat Sep 09, 2006 1:54 am

### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting Speedracer1407 (Thread starter):Yet, a 45 degree crosswind certainly doesn't cause a 45 degree crab angle

Ok, let me throw some numbers out there for you using the trusty old E6-B....all you older pilots remember that don't you? Say you are trying to fly south (180 heading) and have that pesky wind from 225 degrees....45 degrees off your nose. With that wind howling at 20 knots...

A C-172, say approach speed of 65 kts will have to crab into the wind about 12 degrees, so it can fly a heading of 192 to track 180 over the ground.
The same 172 in cruise, say doing 110 kts will only have to crab about 8 degrees.

The faster the aircraft, the less crab.

Now say you go up in your 737 to do touch and goes in the same wind. With an approach speed of say 140 kts the baby Boeing will crab a mere 6 degrees into the wind. Effectively half that of the Cessna on its final approach.

Say your cruising your 737 at 250 kts. (you want to fly low and VFR.   ) With the same conditions you will only be crabbing about 3 degrees.

And as I said earlier, the faster the plane goes, the less crab angle. The faster the wind speed the greater the crab angle.
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CosmicCruiser
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### RE: Crab Angle Vs Crosswind Direction And Speed

 Quoting FredT (Reply 8):In real life, most pilots will hold the controls crossed for a few after liftoff, thus allowing the aircraft to accelerate slightly downwind. Thus, weather waning will not suffice to put the aircraft on the runway track if that is what is desired.

Forgive me for answering in a bit of a rush since I'm starting my countdown before a trip and I'm chasing my tail wrapping up all my "honey dos" but I'm afraid I didn't follow this. When I make a x-wind t/o (and I may tonight judging by the wind outside right now) I hold the crossed controls only long enough to ensure a wings level, nose straight rotation. After that if the clearance was rnwy hdg that's what I fly and the jet will track downwind. I'm sorry but I've never noticed any weather vaneing after liftoff nor on any x-wind ldg while in the air. Maybe there may be some aerodynamic minutae that you're quoting but I'm afraid I'm probably a clumsey old pilot that's never noticed it and should retire. I'll keep my fingers crossed for the next 11 days!! LOL

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