The question Tom had was this: How does a polar change when density altitude is considered?
I posed the broader question: How does density altitude effect speed-to-fly calculations in general?
The problem is that do make this work, the true rate of sink, Vs, must also be replaced by the equivalent rate of sink, using
Vsi=sqrt(r/r0)Vs
The polar is then plotted as Vsi vs. Vi.
This leads Welch, Welch, and Irving to conclude (page 261) that
The performance curve of the glider applies at all altitudes provided that both the forward speed and the rate of sink are "equivalent" speeds.It would appear that polars are unaffected by density altitude.
Furthermore, if wind and actual lift or sink are taken into account, those values are always in terms of true speeds. This makes polars plotted using equivalent speeds essentially useless if one wants to consider the effects of density altitude on glider performance.
Standard Libelle 15m Wing Loading = 350 N/m2 76 (km/h,m/s) data points Angle of Bank: 45 degrees Wind from 000 @ 0 knots; Lift 0 ft/s |
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Density Altitude: 0 ft Minimum Sink 3.4 ft/s at 45 knots Best L/D 26:1 at 60 knots Best Vgrd=60 knots (Vsink=3.8 ft/s) |
Density Altitude: 6000 ft Minimum Sink 3.7 ft/s at 49 knots true (45 indicated) Best L/D 26:1 at 66 knots true (60 indicated) Best Vgrd=66 knots (Vsink=4.2 ft/s) |
Schweizer 1-35 Wing Loading = 293 N/m2 151 (knots,ft/min) data points Angle of Bank: 0 degrees Wind from 000 @ 0 knots; Lift 0 ft/s |
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Density Altitude: 0 ft Minimum Sink 1.9 ft/s at 34 knots Best L/D 38:1 at 48 knots Best Vgrd=48 knots (Vsink=2.1 ft/s) |
Density Altitude: 6000 ft Minimum Sink 2.0 ft/s at 38 knots true (34 indicated) Best L/D 38:1 at 53 knots true (48 indicated) Best Vgrd=53 knots (Vsink=2.3 ft/s) |
PW-5 Wing Loading = 1.00 rel to 1 76 (km/h,km/h) data points Angle of Bank: 0 degrees Wind from 030 @ 20 knots; Lift 0 ft/s |
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Density Altitude: 0 ft Minimum Sink 1.9 ft/s at 35 knots Best L/D 20:1 at 49 knots Best Vgrd=30 knots (Vsink=2.5 ft/s) |
Density Altitude: 6000 ft Minimum Sink 2.1 ft/s at 38 knots true (35 indicated) Best L/D 21:1 at 52 knots true (48 indicated) Best Vgrd=34 knots (Vsink=2.7 ft/s) |
Nimbus II Wing Loading = 1.00 rel to 1 76 (km/h,m/s) data points Angle of Bank: 0 degrees Wind from 005 @ 30 knots; Lift 0 ft/s |
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Density Altitude: 0 ft Minimum Sink 1.1 ft/s at 31 knots Best L/D 19:1 at 59 knots Best Vgrd=29 knots (Vsink=2.5 ft/s) |
Density Altitude: 6000 ft Minimum Sink 1.1 ft/s at 32 knots true (29 indicated) Best L/D 21:1 at 61 knots true (56 indicated) Best Vgrd=31 knots (Vsink=2.4 ft/s) |
Ximango Polar Data Gross Wt = 89728 Pa 101 (knots,ft/min) data points Angle of Bank: 0 degrees Wind from 000 @ 0 knots; Lift -5 ft/s |
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Density Altitude: 0 ft Minimum Sink 7.9 ft/s at 53 knots Best L/D 12:1 at 62 knots Best Vgrd=62 knots (Vsink=8.6 ft/s) |
Density Altitude: 6000 ft Minimum Sink 8.2 ft/s at 58 knots true (53 indicated) Best L/D 13:1 at 66 knots true (60 indicated) Best Vgrd=66 knots (Vsink=8.7 ft/s) |
Discus Wing Loading = 350 N/m2 76 (km/h,m/s) data points Angle of Bank: 5 degrees Wind from 000 @ 0 knots; Lift 0 ft/s Speeds are knots indicated (height loss, radius) are in feet |
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Density Altitude: 0 ft Bank V_Best_L/D V_MinSink Angle (loss, radius) (loss,radius) 30 60 (47.7, 568) 49 (35.1, 368) 45 67 (42.1, 395) 54 (30.3, 258) 60 79 (47.7,322) 64 (34.8,209) |
Density Altitude: 6000 ft Bank V_Best_L/D V_MinSink Angle (loss, radius) (loss,radius) 30 60 (57.0, 668) 48 (41.5, 431) 45 67 (50.3, 472) 54 (36.2, 308) 60 79 (57.0, 386) 64 (41.7, 250) |
Crosscountry (MacCready) Table 76 (km/h,m/s) data points for Janus B Wing Loading = 350 N/m2 Vi (Vcruise) where Vi is the INDICATED speed to fly between thermals and Vcruise is the TRUE cruising speed (true ground speed, taking account of time used to thermal). |
Density Altitude: 0 ft
Climb Lift Encountered During Glide (ft/s) ft/s -3 -3.5 -4 2 65 (15) 66 (14) 68 (13) 1.5 63 (12) 65 (11) 66 (11) 1 62 (9) 63 (8) 65 (8) .5 59 (5) 62 (4) 63 (4) Density Altitude: 6000 ft
Climb Lift Encountered During Glide (ft/s) ft/s -3 -3.5 -4 2 64 (16) 65 (15) 66 (14) 1.5 62 (13) 64 (12) 65 (11) 1 60 (9) 62 (8) 64 (8) .5 58 (5) 60 (4) 62 (4)
stdtemp=stdtemp0 * (1 - densalt/145442) stdpres=stdpres0 * (1 - densalt/145442)5.255876 r/r0 = s = (1 - densalt/145442)4.255876
Bob Hanson