Gliding distance and winds aloft

[flyingcheesehead]

It's been a while but I ran some calculatons to see what effect the winds had on the minimum altitude necessary to remain within gliding distance and if memory serves (a depressingly rare occurance these days) the wind has virtually no influence on that. It certainly changes the decision point but I think that's about it. To get accurate abou this you have to consider the changes in best glide speed with wind (which shifts the origin of the L/D curve on which best glide is based). If I get bored I might try to run through the math again and see if my memory is good or bad.

Lance,

I was using a fairly simple groundspeed/sink calculation. Best glide for me is something like 80 kt and 1000fpm sink (not looking at actual numbers here). With a 50kt wind out of the west, that means 30kt westbound and I'd have to be within 6.25 miles of shore to make it into the wind from 13,000 MSL (roughly 12,500 AWL) (though this could be increased by flying faster than "best" glide).

However, eastbound would be 130kt for 12.5 min or about 27nm. So, that removes most of the exposure (33nm out of about 40-45 depending on the crossing location). Again, minimum sink airspeed would be a better choice here.

Doesn't work for this particular example, but it actually did for the numbers I had at the time. I was also compensating for the varying winds aloft at the various altitudes.

I guess the extreme example would be with a wind speed approaching Vne (It'd be somewhat less due to the downward angle of the airplane at Vne.) Your decision point would be at the western shore, and if your engine failed right there you'd have to point your nose down and go really fast (airspeed) to get zero groundspeed and land right on the shore. However, you'd be doing something like 275kt at minimum sink and be able to glide for 57nm eastbound, plenty to make it across the lake.

You mention shifting the origin of the L/D curve on which best glide is based, I assume you are talking about the effects of headwind/tailwind component on the actual over-ground best glide distance (Higher Vg for headwind, lower for tailwind)?

 

[EdFred]

http://webpages.charter.net/edfred/flying/makefield.xls

Should be able to mess with numbers there.

 

[Lance F]

The horizontal component of the winds has no effect on the best glide speed or the minimum sink rate speed. There is an optimum for both at any given weight. That said the distance you can go at that best glide speed is directly dependent on wind speed. Let's say your best glide speed is 100 knots and the glide ratio is 10:1. With 0 kts wind speed from 5280' up you will (theoretically) glide 10 miles. With 100 kts ! on the nose all the way down you will go 0 miles.

The vertical component is a different story. To keep it simple: speed up in sink and slow down (but not less than best glide speed) in lift.

 

[flyingcheesehead]

The horizontal component of the winds has no effect on the best glide speed or the minimum sink rate speed. There is an optimum for both at any given weight. That said the distance you can go at that best glide speed is directly dependent on wind speed. Let's say your best glide speed is 100 knots and the glide ratio is 10:1. With 0 kts wind speed from 5280' up you will (theoretically) glide 10 miles. With 100 kts ! on the nose all the way down you will go 0 miles.

But if you do have wind, and you don't have a choice as to which direction to go (ie over the lake) except the one that takes you to shore...

Well, say you have a 60kt headwind and your best glide is 60 knots. You'll go straight down at best glide, but if you go faster, you'll go somewhere even though your glide ratio through the air will be reduced due to increased drag.

Right?

The lake is kind of a special case. Unless you've got a turbo and oxygen, it's pretty difficult to climb high enough to remain within gliding distance of one side or the other. It's about 45nm across at the "narrow" parts. The water is about 570 MSL IIRC. So, for zero exposure at zero wind, an 8:1 glide would require you to climb to 17,700 MSL. (IIRC, an average GA airplane glide ratio is 9:1, but that assumes perfect conditions and piloting skills, which I don't have.) Even 10:1 would require 14,300 MSL.

 

[gismo]

The horizontal component of the winds has no effect on the best glide speed or the minimum sink rate speed.

Not so. The no wind best glide is equal to the airspeed at the tangent of a line from the origin of a graph of airspeed vs sink rate (which IIRC happens to be the same as the graph of lift vs drag). Wind has the effect of shifting the origin along the airspeed axis by the amount of wind which also changes the slope of the tangent line and therefore the airspeed at the tangent.

As Kent pointed out this speed is never less than the min sink speed (bottom of the curve) but it approaches min sink as the origin moves further and further away from the curve bottom. In a headwind the line gets steeper and steeper as it follows the curve of rapidly increasing drag at higher airspeeds and the tangent speed eventually reaches Vne when the wind itself comes close to Vne (the wind speed needed to make best glide equal to Vne is somewhat less than Vne or the slope of the curve would have to be vertical).

 

[gismo]

But if you do have wind, and you don't have a choice as to which direction to go (ie over the lake) except the one that takes you to shore...

Well, say you have a 60kt headwind and your best glide is 60 knots. You'll go straight down at best glide, but if you go faster, you'll go somewhere even though your glide ratio through the air will be reduced due to increased drag.

Right?

Right.

The lake is kind of a special case. Unless you've got a turbo and oxygen, it's pretty difficult to climb high enough to remain within gliding distance of one side or the other. It's about 45nm across at the "narrow" parts. The water is about 570 MSL IIRC. So, for zero exposure at zero wind, an 8:1 glide would require you to climb to 17,700 MSL. (IIRC, an average GA airplane glide ratio is 9:1, but that assumes perfect conditions and piloting skills, which I don't have.) Even 10:1 would require 14,300 MSL.

The narrow crossing near Traverse City is just under 40 NM (46SM) and the slicker airplanes (Bonanza, Mooney, maybe Cirrus) are closer to 11.5:1 (2 SM/1000 ft) so to reach the shore from the middle you'd only need to be at about 12,500 MSL. Down by Ludington where it's 44 NM 13,500 would do. Typically, the slicker airplanes also have higher service ceilings making these altitudes attainable most of the time. When I used to fly a Bonanza across the lake I was able to climb high enough to eliminate being out of reach of land. The biggest downside was that when westbound with a strong westerly breeze it could add a half hour or more to climb that high.

 

[gismo]

Lance,

I was using a fairly simple groundspeed/sink calculation. Best glide for me is something like 80 kt and 1000fpm sink (not looking at actual numbers here). With a 50kt wind out of the west, that means 30kt westbound and I'd have to be within 6.25 miles of shore to make it into the wind from 13,000 MSL (roughly 12,500 AWL) (though this could be increased by flying faster than "best" glide).

However, eastbound would be 130kt for 12.5 min or about 27nm. So, that removes most of the exposure (33nm out of about 40-45 depending on the crossing location). Again, minimum sink airspeed would be a better choice here.

Doesn't work for this particular example, but it actually did for the numbers I had at the time. I was also compensating for the varying winds aloft at the various altitudes.

Not only does it not work, it doesn't hardly help per your own calculations. With no wind you'd be OK crossing 32 NM @12,500 vs 33 NM with a 50 Kt wind.

I guess the extreme example would be with a wind speed approaching Vne (It'd be somewhat less due to the downward angle of the airplane at Vne.) Your decision point would be at the western shore, and if your engine failed right there you'd have to point your nose down and go really fast (airspeed) to get zero groundspeed and land right on the shore. However, you'd be doing something like 275kt at minimum sink and be able to glide for 57nm eastbound, plenty to make it across the lake.

I think if you used real numbers you'd find that the result would be a lot less than 57NM. Perhaps there is an improvement with wind with an airplane that only glides 1.25 SM/1000 ft. In any case my ages ago analysis was done using the performance of the Bonanza I owned at the time which had a glide ratio of 2 SM/1000 ft.

You mention shifting the origin of the L/D curve on which best glide is based, I assume you are talking about the effects of headwind/tailwind component on the actual over-ground best glide distance (Higher Vg for headwind, lower for tailwind)?

Yep. See my other post on that.