Help calculating Speed To Fly for headwind and tailwind

I am looking for the equations to determine the speed to fly for a
headwind or tailwind. I can calculate the the speed to fly for no
wind based on the polar from Equation V (Page 106, 1988 US Version) in
Reichmann. He gives a graphical method to determine the speeds for a
headwind or tailwind but I would like to translate this into an
equation.

I can do it by shifting the polar to the "true" ground speed, but then
I have to correct the predicted STF from the equation by adding or
subtracting the wind again. I'm not sure if this is the best way to do
it.

Anyone have a good set of equations or example of how to do this
simply?

Thanks,

Tim

On May 27, 10:49*pm, Tim Taylor wrote:

Anyone have a good set of equations or example of how to do this
simply?


The fastest speed through the air mass will give the fastest speed
over the ground. The wind does not change the speed to fly. It only
impacts best glide speed to a landing.

So add 0xW for a headwind and subtract 0xW for a tailwind.

Andy

On May 28, 6:02*am, Andy wrote:
On May 27, 10:49*pm, Tim Taylor wrote:

Anyone have a good set of equations or example of how to do this
simply?

The fastest speed through the air mass will give the fastest speed
over the ground. *The wind does not change the speed to fly. *It only
impacts best glide speed to a landing.

So add 0xW for a headwind and subtract 0xW for a tailwind.

Andy

I think Tim means STF for final glide where you are flying in
reference to the ground, not the airmass. John Cochrane's analysis
shows that you have different lift strength targets for upwind/
downwind turnpoints as well, though I don't know if this extends to
STF. John?

I have the final glide formulae in a spreadsheet, including effects of
wind and wing loading, if you are interested.

9B

On May 28, 7:10*am, Nine Bravo Ground wrote:
On May 28, 6:02*am, Andy wrote:

On May 27, 10:49*pm, Tim Taylor wrote:

Anyone have a good set of equations or example of how to do this
simply?

The fastest speed through the air mass will give the fastest speed
over the ground. *The wind does not change the speed to fly. *It only
impacts best glide speed to a landing.

So add 0xW for a headwind and subtract 0xW for a tailwind.

Andy

I think Tim means STF for final glide where you are flying in
reference to the ground, not the airmass. John Cochrane's analysis
shows that you have different lift strength targets for upwind/
downwind turnpoints as well, though I don't know if this extends to
STF. John?

I have the final glide formulae in a spreadsheet, including effects of
wind and wing loading, if you are interested.

9B

To clarify, the ground reference STF is reserved for trying to
maximize distance, not speed. This means that your 4-knot final glide
is at the same speed irrespective of wind up until the best glide STF
accounting for wind exceeds the McCready STF - at that point you won't
make it home into the wind unless you speed up. That would only apply
in situations where you make a downwind turnpoint under weak
conditions with enough altitude to get home but without strong enough
lift to make sustained headway - that's only happened to me once - 1.5
knot thermals and a 40 mph headwind (I landed).

I think you could use a version of this logic in making an upwind
turnpoint - though again I think the situation would be rare. In this
case you are calculating your angle over the ground to see if you can
make the turnpoint before you need to take a thermal. I suppose it is
possible that the optimal solution is that you need to fly faster than
McCready speed to make the turnpoint, but I think that means that
you'd be unable to make sustained headway given the thermal strength.
Maybe if you were trying to duck into a turnpoint at the edge of a big
downburst or something.

9B

On May 28, 10:10*am, Nine Bravo Ground wrote:
On May 28, 6:02*am, Andy wrote:

On May 27, 10:49*pm, Tim Taylor wrote:

Anyone have a good set of equations or example of how to do this
simply?

The fastest speed through the air mass will give the fastest speed
over the ground. *The wind does not change the speed to fly. *It only
impacts best glide speed to a landing.

So add 0xW for a headwind and subtract 0xW for a tailwind.

Andy

I think Tim means STF for final glide where you are flying in
reference to the ground, not the airmass. John Cochrane's analysis
shows that you have different lift strength targets for upwind/
downwind turnpoints as well, though I don't know if this extends to
STF. John?

I have the final glide formulae in a spreadsheet, including effects of
wind and wing loading, if you are interested.

9B

If you want to derive the formula you need a little bit of 1st year
calculus plus some algebra. Derive a line passing through
the point (-headwind, -MC) that is tangent to your polar. The slope
will be equal to the 1st derivative of the polar at the speed to fly.
I use it often enough when analyzing the performance of gliders
I fly (I've made more than a few prayer wheels in my day).

As far as speed to fly, Andy is correct. Fly through the airmass at
your MC speed. John's paper says you should nudge your MC
a bit up or down when you're flying into our out of an upwind
turnpoint (read the paper for details).

For final glide, THEN you can take the headwind into account.

-- Matt

On May 28, 6:02*am, Andy wrote:

*The wind does not change the speed to fly. *It only
impacts best glide speed to a landing.

To be more clear I should have said the wind only impacts speed for
best glide range to a landing. There are of course also cases where
the next thermal cannot be reached unless wind is taken into account
but that too is a best range solution not a best speed solution.

Andy

On May 28, 11:26*am, Andy wrote:
On May 28, 6:02*am, Andy wrote:

*The wind does not change the speed to fly. *It only
impacts best glide speed to a landing.

To be more clear I should have said the wind only impacts speed for
best glide range to a landing. *There are of course also cases where
the next thermal cannot be reached unless wind is taken into account
but that too is a best range solution not a best speed solution.

Andy

Thanks for all the help and suggestions. I was mixing equations too
late at night. Here is the data from the spreadsheet for a Standard
Class glider in MPH.

My understanding from reviewing the theory is these are applicable for
all legs and not just the last. Looks like using about half the wind
speed would be a good rough approximation for most normal speeds.

MC Headwind Zero Tailwind
30 20 10 0 -10 -20 -30
0 71 65 61 58 55 54 52
1 84 77 72 67 64 62 60
2 94 87 81 76 72 69 66
3 103 95 89 84 79 75 72
4 111 103 96 91 86 82 78
5 118 110 103 97 92 88 84
6 125 117 110 103 98 93 89
7 131 123 116 109 103 98 94
8 137 129 121 115 109 103 99
9 143 134 127 120 114 108 104
10 148 139 132 125 119 113 108

On May 28, 8:20*pm, Tim Taylor wrote:
On May 28, 11:26*am, Andy wrote:

On May 28, 6:02*am, Andy wrote:

*The wind does not change the speed to fly. *It only
impacts best glide speed to a landing.

To be more clear I should have said the wind only impacts speed for
best glide range to a landing. *There are of course also cases where
the next thermal cannot be reached unless wind is taken into account
but that too is a best range solution not a best speed solution.

Andy

Thanks for all the help and suggestions. *I was mixing equations too
late at night. *Here is the data from the spreadsheet for a Standard
Class glider in MPH.

My understanding from reviewing the theory is these are applicable for
all legs and not just the last. *Looks like using about half the wind
speed would be a good rough approximation for most normal speeds.

MC * * *Headwind * * * * * * * *Zero * * * *Tailwind
* * * * 30 * * *20 * * *10 * * *0 * * * -10 * * -20 * * -30
0 * * * 71 * * *65 * * *61 * * *58 * * *55 * * *54 * * *52
1 * * * 84 * * *77 * * *72 * * *67 * * *64 * * *62 * * *60
2 * * * 94 * * *87 * * *81 * * *76 * * *72 * * *69 * * *66
3 * * * 103 * * 95 * * *89 * * *84 * * *79 * * *75 * * *72
4 * * * 111 * * 103 * * 96 * * *91 * * *86 * * *82 * * *78
5 * * * 118 * * 110 * * 103 * * 97 * * *92 * * *88 * * *84
6 * * * 125 * * 117 * * 110 * * 103 * * 98 * * *93 * * *89
7 * * * 131 * * 123 * * 116 * * 109 * * 103 * * 98 * * *94
8 * * * 137 * * 129 * * 121 * * 115 * * 109 * * 103 * * 99
9 * * * 143 * * 134 * * 127 * * 120 * * 114 * * 108 * * 104
10 * * *148 * * 139 * * 132 * * 125 * * 119 * * 113 * * 108

I'm not sure this is right Tim, unless you are thinking it is for a
special case like upwind/downwind turnpoints - and even then I'm not
sure.

John Cochrane's paper is a bit ambiguous on the point of speed to fly
versus how strong a thermal to take in the up/downwind turnpoint
scenario and I'm not totally clear on to what extent (or whether)
McCready theory accounts for wind drift while thermalling - even after
reading John's paper. If you are flying into a downwind turnpoint the
idea is you should be willing to take relatively weaker thermals to
get high so you don't have to do as much climbing into the wind after
making the turn.

Where I get into trouble thinking about this is that I can easily
glide 40 or 50 miles into a downwind turnpoint and I don't think I
should PLAN on taking a relatively weaker thermal - therefore my STF
should set to whatever my EXPECTED next climb will be heading into the
turn. As I get closer to the turn I may start dialing back my
expectations for the climb I'm going to find in the remaining
distance, depending on how things look ahead, how many miles I have to
the turn, etc. As I do that I suppose I would also slow down to
optimize the overall cruise/climb combination. I stop dialing back
McCready at the point that my expectations for post-turn (into the
wind) thermal give me a better overall time than my expectations for a
pre-turn (downwind) thermal.

Example: I'm heading into the (20 mph) downwind turn at 5,000 AGL and
am 5 miles out. It's a day with 5 knot typical climbs and occasional
10-knotters. So let's say I'm flying McCraedy 5. Looking at John's
chart I should be willing to take anything stronger than about 2.5
knots while heading downwind into the turn so presumably I am
progressively slowing down as my expectations for the lift I'm going
to find in the shortening distance go from 5 knots down to 2.5 knots -
my minimum. At some point I may realize I'm not going to get another
climb before the turn. In that case what do I do? Since I have plenty
of altitude, my climb expectations go from 2.5 knots (pre-turn) back
up to 5 knots (post-turn). Do I speed up or do I fly based on a ground-
fixed polar until I make the turn?

I'm pretty sure once I make the turn I am back to flying Mc=5 to
optimize my speed versus the airmass.

The logic is analogous but different for an upwind turnpoint. Here I
assume I am flying Mc=5 until I can reach the turnpoint with some
reasonable altitude left to find a decent thermal. Using John's chart,
I don't want to take any thermals weaker that 9 knots or so. Does that
mean I should fly Mc=5 until I think I can make the turnpoint flying
Mc=9 and then speed up to the STF for Mc=9? Presumably I will be low
at the turn, but high enough that I plan on running into at least a 5-
knot thermal. After the turn should I slow down to Mc = 5?

That seems like a lot of gear-shifting. The alternative possibility is
that the optimal thing to do is fly the same McCready speed (Mc=5),
but be pickier about what lift you take into the wind and less picky
downwind. It seems like once you make the turn you are back to
ignoring the wind since all cruise and climb will be subjectt to the
same wind vector and the STF that yields the fastest speed through the
airmass will also yield the fastest speed over the ground.

Thoughts?

9B

Thoughts?

9B

Here's my 2 cents.

If you're racing, not maximizing glide over the ground, and if you're
far from a turnpoint -- meaning you will certainly have to thermal
before you get to the turnpoint -- then as everybody notes, the wind
speed is irrelevant.

That assumes that thermals drift with the wind, and are as easy to
core going upwind as downwind. Thermals actually drift a bit slower
than the wind, and are anchored to ground sources. That means that
going upwind is harder; you're effectively in a lower-performing
glider, so in fact you have to fly more cautiously. I seem to have an
easier time centering when going downwind as well; that may be because
I hit the obvious core first rather than be seduced by the driblets
off downwind of the core. I also seem to stay in contact with streets
better going downwind. (In general, better performing gliders use
slightly higher Mc settings, because they are less likely to get in
trouble)

But back to theory which ignores all this stuff. The calculations in
"upwind/downwind" assume you're near the turnpoint. Here you're
making the decision "do I climb at x before the turnpoint or do I
wait, round the turnpoint and climb at y?" It's only valid if the
latter is an option before hitting the ground!

In any decent wind, it's surprising how much difference there is
between x and y. On the other hand, the graph quantifies common sense:
if you are in an 8 knot thermal and all the other thermals are 3
knots, take it even if it's upwind! The rule of thumb about turning
upwind low isn't always right.

I bug the clearnav team to put these numbers in about once a week.
When you're above glideslope to the next turnpoint, it could show the
equivalent Mc "after the turn" to your current Mc. So far no luck, but
they may correctly perceive that there are about 3 of us who
understand and care about this number.

Many people make the mistake of thinking wind affects final glide. It
does not (except for the above meteorological considerations). There
does come a point, gliding in to the wind, that lowering your
MacCready setting actually results in a worse glide. You'll see that
-- you get low, turn down the Mc, and all of a sudden you're even
lower! ouch!

If that isn't enough, you need a thermal, and the thermal has to be
stronger than this minimum Mc setting. If you're going downwind, a
slightly negative Mc setting will result in a better glide. I also
encourage my favorite insturment makers to not allow the Mc setting to
go below the value that gives the best glide over the ground, and
allow it to go slightly negative downwind. Again, I think they rightly
perceive this as unnecessary nerdiness.

In both cases, there really is no valid reason at all for cruising at
a lower Mc setting than the weakest (smooth, bottom to top average,
including all centering etc) thermal you'd take. Equivalently, if
you're cruising at Mc 2 and the weather gods grant you a smooth,
guaranteed 3 knot thermal, you're better off taking it and then
cruising at Mc 3 for a while. This is very hard to swallow, but it's
true.

John Cochrane

On May 29, 12:22*pm, John Cochrane
wrote:
Thoughts?

9B

Here's my 2 cents.

If you're racing, not maximizing glide over the ground, and if you're
far from a turnpoint -- meaning you will certainly have to thermal
before you get to the turnpoint -- then as everybody notes, the wind
speed is irrelevant.

That assumes that thermals drift with the wind, and are as easy to
core going upwind as downwind. Thermals actually drift a bit slower
than the wind, and are anchored to ground sources. That means that
going upwind is harder; you're effectively in a lower-performing
glider, so in fact you have to fly more cautiously. *I seem to have an
easier time centering when going downwind as well; that may be because
I hit the obvious core first rather than be seduced by the driblets
off downwind of the core. I also seem to stay in contact with streets
better going downwind. (In general, better performing gliders use
slightly higher Mc settings, because they are less likely to get in
trouble)

But back to theory which ignores all this stuff. The calculations in
"upwind/downwind" assume you're *near the turnpoint. Here you're
making the decision "do I climb at x before the turnpoint or do I
wait, round the turnpoint and climb at y?" *It's only valid if the
latter is an option before hitting the ground!

In any decent wind, it's surprising how much difference there is
between x and y. On the other hand, the graph quantifies common sense:
if you are in an 8 knot thermal and all the other thermals are 3
knots, take it even if it's upwind! *The rule of thumb about turning
upwind low isn't always right.

I bug the clearnav team to put these numbers in about once a week.
When you're above glideslope to the next turnpoint, it could show the
equivalent Mc "after the turn" to your current Mc. So far no luck, but
they may correctly perceive that there are about 3 of us who
understand and care about this number.

Many people make the mistake of thinking wind affects final glide. It
does not (except for the above meteorological considerations). There
does come a point, gliding in to the wind, that lowering your
MacCready setting actually results in a worse glide. You'll see that
-- you get low, turn down the Mc, and all of a sudden you're even
lower! ouch!

If that isn't enough, you need a thermal, and the thermal has to be
stronger than this minimum Mc setting. If you're going downwind, a
slightly negative Mc setting will result in a better glide. *I also
encourage my favorite insturment makers to not allow the Mc setting to
go below the value that gives the best glide over the ground, and
allow it to go slightly negative downwind. Again, I think they rightly
perceive this as unnecessary nerdiness.

In both cases, there really is no valid reason at all for cruising at
a lower Mc setting than the weakest (smooth, bottom to top average,
including all centering etc) thermal you'd take. Equivalently, if
you're cruising at Mc 2 and the weather gods grant you a smooth,
guaranteed 3 knot thermal, you're better off taking it and then
cruising at Mc 3 for a while. This is very hard to swallow, but it's
true.

John Cochrane

A common thread in this discussion is the need to know the
ACTUAL average climb over an entire thermal. Otherwise
you're typically plugging too high a number into McCready
theory, which doesn't work.

For you SN10 pilots, this is why the instruments I've
designed prominently display TAv - Thermal Average...
Use it ! Don't use the 20 second averager peak...

For John, perhaps time to switch back ;-)
And if you don't, you can still use the SN10 in my
plane to plan your task on the ramp ;-)

Hope this helps,
Best Regards, Dave "YO electric"