Paraglider Performance Comparision

Paraglider Performance Comparison
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Definitions

MSL : Mean Sea Level. The average level of the oceans.

Grade : This value is not obtained from the source of information (magazine). It is calculated by an internal function written by myself, to represent how well a wing performs, considering your bias in performance reference points, and the spectrum for those values amongst all listed wings. For each characteristic (Sink rate, Best L/D, Max speed), the minimum and maximum values for all wings are established to determine the range of possible values, allowing to rank a given characteristic for a given wing. By specifying what is most important (weighting factor) to you, for example :

7 out of 10 for the Minimum Sink Rate. 0 would mean you don't care for this.
10/10 for the Maximum GR_W.
6/10 for the Maximum Speed.

the function can derive a global performance value which corresponds to your vision of an ideal wing. Just like a grade in school, a low grade doesn't mean a wing is good for nothing, just that it is worse than the others it is compared to.
Missing information : In the event that a criterion's value ( like the GR_W ) can not be calculated for a given wing, a value corresponding to 25% of the range for all wings is assumed (typically conservative).

Universal Rating : In order to deal with the various classification systems ( DHV, AFNOR, and EN ), an independent scale is used here.

Universal Rating	DHV, AFNOR, EN rating obtained (worst of all wing sizes).
1	DHV 1 and AFNOR [Undetermined/Standard/Performance/Compétition] EN A
1.5	DHV 1-2 and AFNOR [Undetermined/Standard/Performance/Compétition] DHV [Undetermined] and AFNOR Standard EN B
1.75	DHV 2 and AFNOR Standard
2	DHV 2 and AFNOR [Undetermined/Performance] EN C
2.5	DHV 2-3 and AFNOR [Undetermined/Performance/Compétition] DHV [Undetermined/2-3/3] and AFNOR Performance EN D
3	DHV 3 and AFNOR [Undetermined/Compétition] DHV [Undetermined/3] and AFNOR Compétition
4	None

Letters following the value, indicate the original rating systems which were applied to the wing. Examples :

Universal Rating indicated in table.	DHV, AFNOR rating obtained.
1-D	DHV 1
1-E	EN A
1.5-D	DHV 1-2
1.5-A	AFNOR Standard
1.5-E	EN B
1.5-DA	DHV 1-2 and AFNOR Standard
1.75-DA	DHV 2 and AFNOR Standard
2-D	DHV 2
2-E	EN C
2-DA	DHV 2 and AFNOR Performance
2.5-D	DHV 2-3
2.5-E	EN D
2.5-A	AFNOR Performance
2.5-DA	DHV 2-3 and AFNOR Performance
3-D	DHV 3
3-A	AFNOR Compétition
3-DA	DHV 3 and AFNOR Compétition
4-	None

Correction Labels : The following characters may appear in the table :

L : Data has been corrected (normalized) for wing Loading. See also TFW - Test.
T : Data has been corrected (normalized) for Temperature. See also Atmospheric Conditions - Temperature.
A : Data has been corrected (normalized) for Altitude. See also Atmospheric Conditions - Altitude.
P : Data has been corrected (normalized) for MSL Pressure. See also Atmospheric Conditions - MSL Pressure.

Correction Formulas :

Variables, Subscripts, extensions :

TFW : TFW (kg).
T : Temperature (°C).
z : Altitude (m).
P : Pressure (kPa).
D : Air density (kg/m³).
V : Speed (km/h). This can also apply to sink rate (m/s).
1,2 : 1 reffers to a non-corrected state, 2 for corrected. For example : T₁ is the temperature of the air during the reviewer's test. T₂ is the temperature of the air that you want values normalized for.
_msl : Indicates that the value is taken at MSL. For example : T_msl : is the temperature of the air at MSL.
_avg : Indicates an average. For example : T_avg : is an average temperature.

The following is the sequence of formulas used to establish the corrections.

From the test conditions, we know : TFW, T, z, and P_msl.
Determine the temperature at MSL.
k = 0.0065 °C/m
T_msl (°C) = T + k . z
Determine the average temperature between MSL and the altitude of the test.
T_avg (°C) = ( T - T_msl ) / ln( ( T + 273.15 ) / ( T_msl + 273.15 ) ) - 273.15
Note that ln() is the natural logarithm function.
Determine the pressure at the location where the test was done.
P (kPa) = P_msl . e^{{[-0.02896 . 9.8 / 8.314] . [z / (T_avg + 273.15)]}}.
Note that "e" is a constant equal to 2.7182818 .
Determine the air density at the location where the test was done.
D (kg/m³) = 0.02896 . P / [ 8.314 ( T + 273.15 ) ]
With the above formulas, we can establish : D₁ , D₂ . And for the different TFW we have : TFW₁ , TFW₂ .
We can now determine the correction for speed (and sink rate) as :
V₂ (same units as V₁) = V₁ [ ( D₁ . TFW₂ ) / ( D₂ . TFW₁ ) ] ^1/2

Sink Rate : It is the vertical speed within the air mass. See variable V in Polar Curve.

Speed on Trajectory : This is the air speed along your flight path (trajectory) within the air mass. It is not the same as the horizontal air speed. For more information on the difference, see variable D in Polar Curve.

Stall Speed : This value is the Speed on Trajectory at which the wing will stall. This is NOT the minimum speed at which it is still safe to fly this wing.

Trim Speed : This value is the maximum Speed on Trajectory without using the accelerator.

Max Speed : This value is the maximum Speed on Trajectory using the accelerator.

Speed Range : This value is calculated (not taken from the magazine) as :
(Speed Range) = (Max Speed) - (Stall Speed)

Polar Curve : It is the plot of a wing's sink rate (Y axis, pointed down) as a function of the horizontal air speed (X axis). The following are some transformations that can be performed on a given curve data point's coordinates :
      Variables (use consistant units for speed in calculations) :
           V : speed along the Vertical axis.
           H : speed along the Horizontal axis.
           D : Speed on Trajectory (Diagonal).
           F : lift/drag (Finesse in French).
      Equations :
           H = sqrt( D² - V² )
           H = F . V
           V = D / sqrt( 1 + F² )       or       D = V . sqrt( 1 + F² )
Note that magazines (and pilots) usually report speed as D instead of H.
For a smooth curve plot, a Polar Curve - Natural Cubic Spline is used.

Polar Curve - Input Format : It is a string (of characters) used to define points along the Polar Curve. It is used in the Extra Wing definition. Format rules :

| is used to delimit data points.
, delimits data point coordinates.
d identifies that the number immediatly following is a Speed on Trajectory (Diagonal) expressed in km/h. This will be the 1st coordinate for the data point.
v identifies that the number immediatly following is a Sink Rate (m/s) along the Vertical axis. This will be a 2nd coordinate for the data point.
f identifies that the number immediatly following is Lift/Drag (Finesse) ratio. This will be a 2nd coordinate for the data point.
S as the 3rd coordinate, identifies this point as the Stall Speed.
T as the 3rd coordinate, identifies this point as the Trim Speed.
M as the 3rd coordinate, identifies this point as the Max Speed.

Example : "d22.5,,S|d29,v1.05|d35,,T|d37,f8.3|d45,v2.2,M"

d22.5,,S Stall Speed is 22.5 km/h.
d29,v1.05 Sink Rate of 1.05 m/s for Speed on Trajectory of 29 km/h.
d35,,T Trim Speed is 35 km/h.
d37,f8.3 Lift/Drag of 8.3 for Speed on Trajectory of 37 km/h.
d45,v2.2,M Sink Rate of 2.2 m/s for Speed on Trajectory of 45 km/h, which is also the Max Speed.

Polar Curve - Natural Cubic Spline : If desired, a Natural (free slope at endpoints) Cubic Spline is fitted through the measured data points, when there are at least 4. This allows to show the Polar Curve as a smooth curve, and provide better resolution to establish the GR_W. Note that when using such interpolation, we may generate better performance figures than those based on the measurement points alone.

GR_W : It is the Glide Ratio (with respect to ground tracking, not just Lift/Drag) with a headwind speed of W. It is established by finding the point on the Polar Curve which produce the best glide for the given headwind. Notes :

Typically W = 20 km/h, as this corresponds to a typical summer mountain breaze, to a ridge lift wind speed sufficient to keep you up, and to a paraglider's stall speed.
If there is no value shown in the table, it is because it could not be determined with sufficient certainty. This will lower the Grade. This is the case when the head wind value (W) is too close to the Speed on Trajectory of the last measured data point on the Polar Curve and that the Max Speed is either undefined or indicates a lack of data at high speed (often the case with data from Parapente Mag). Typically, if you lower the head wind (W), more values will be valid.
When W=0 (no wind), the best GR_W value for the wing, is the same as the best Lift/Drag value for the wing.
A better value can be determined when a Polar Curve - Natural Cubic Spline can be applied.

Wing Loading : Wing loading is the TFW divided by the wing's area when laid flat (not the projected area).

TFW (Total Flying Weight) : The weight of all that flies : Yourself, your worries, your clothes, harness, ballast, risers, lines, and wing.

TFW - Minimum : This is the minimum TFW recommended by the manufacturer.

TFW - Maximum : This is the maximum TFW recommended by the manufacturer.

TFW - Test : This is the TFW during the test. This value is used to standardize the data for wing loading within the specified weight range. To accomplish this, we need to collect these 3 pieces of information for each wing : Minimum and maximum total flying weight (TFW) according to the manufacturer, total flying weight used during the test. Because speed (and sink rate) only change by the square root of the ratio of the TFW (see Correction Formulas), and that the test pilot can not be more than half of the TFW range away from the ideal TFW, this only leads to small speed variations though. For example : On the wing with a TFW range of 90 to 110 kg, a test pilot with a TFW of 90 kg that registered a speed of 40 km/h would be corrected as (TFW = 100 kg) 42.2 km/h .

Atmospheric Conditions - Temperature : Air temperature during the test. OACI (Organisation de l'Aviation Civile Internationale) standard temperature is 15 °C (59 °F).

Atmospheric Conditions - Altitude : Altitude associated to the test. This value can have been taken at launch or at the time of the actual measurements.

Atmospheric Conditions - MSL Pressure : MSL air pressure during the test. OACI (Organisation de l'Aviation Civile Internationale) standard MSL pressure is 101.325 kPa.

Model Name Query - Format : It is a string (of characters) used to limit the wings displayed in the final output table. Format rules :

An empty string will allow all wings to be considered (no filtering).
The search is case insensitive. So it does not matter if you use uppercase or lowercase letters.
Use blank space characters to separate desired wing model names.
"." characters will be substituted for a blank character when comparing to a wing's model name : "Astral.2" will find a match with model name "Astral 2".
Supplied wing model names can be a subset of their true name (but must begin the same way) : "Astral" will allow to accept "Astral" or "Astral 2" as valid wing models.

Example : "Astral OmEgA.4" ==> We will find these valid wing model names : "Astral", "Astral 2", "Omega 4".

Source : This is where the performance measurements are taken from :

"VL" : Vol Libre . Click the logo for more information.
"PM" : Parapente Mag . Click the logo to visit their home page.
"Extra" : The Extra Wing data you entered.
"Manufacturer" : A wing manufacturer. Examples : "Advance", "Apco", "Nova",... Or anyone that could profit from selling the wing model tested.
Manufacturers can contribute, see You can be a test pilot !
"Pilot's Name" : The name of a Pilot. He has no bias with respect to the Manufacturer of the wing tested.
Pilots can contribute, see You can be a test pilot !