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#1
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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 |
#2
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Help calculating Speed To Fly for headwind and tailwind
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 |
#3
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Help calculating Speed To Fly for headwind and tailwind
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 |
#4
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Help calculating Speed To Fly for headwind and tailwind
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 |
#5
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Help calculating Speed To Fly for headwind and tailwind
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 |
#6
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Help calculating Speed To Fly for headwind and tailwind
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 |
#7
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Help calculating Speed To Fly for headwind and tailwind
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 |
#8
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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 |
#9
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Help calculating Speed To Fly for headwind and tailwind
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 |
#10
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Help calculating Speed To Fly for headwind and tailwind
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" |
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