Help calculating Speed To Fly for headwind and tailwind

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