Useful Calculations and Conversions  for Hang Gliders and Paragliders

  By Ulf Arndt, February 2003

Time to switch on your onboard computer for this section. What sets apart top pilots from ordinary gravity bound earthlings, is that they have more of the ability to be multitasking and do many things at the same time in parallel. Like analyzing what goes on around you. And make use of the info that the GPS and Vario give you. Ordinary folks can do 7 tasks at a time; fighter pilots can do 15 or more.  While you fly, you feel your reaction of your wing, control it, watch out in the sky what the others are doing, monitor the clouds and how they develop, look at the cloud shadows , observe your GPS ground speed, compare it with your Vario sink and climb, adjust the toggles, maybe play a bit with the speed bar, listen a bit on what the other talk about on the radio and maybe also give a position report to your recovery , … and every few seconds make the correct decisions. If you get it wrong you find yourself on the ground after a few minutes.

In 1980 ( well before Paragliding was around)  a  top glider pilots stated  that with a sailplane one has to make every minute a correct decision to stay up.

Well, with a Paraglider I  reckon it is more stress, something like every 10 seconds.

Airspeed, Windspeed,Groundspeed and GPS

Groundspeed GS  = Airspeed AS  + Windspeed WS

 when you fly downwind your GPS will show a GSd = AS + WS
 when you fly intowind your GPS will show a GSi = AS - WS
Assuming your toggle settings are the same.

With your GPS on you can easily determine your trim speed and the wind speed by flying first into wind , hands up and find the slowest speed.
Then turn around and  fly downwind, hands up and find the fastest speed.

   Your trim speed TS will be (GSd + GSi) / 2

   And the wind speed WS will be (GSd-GSi) / 2

   downwind 50 km/h  , into wind  20 km/h

     trim speed = ( 50 +20) /2  = 70/2 = 35
    wind speed = ( 50-20) / 2 ) = 30/2 = 15 km/h

 Distances , Speeds

  1 Nautical mile is 1.8652 km,  to convert from NM to km ,  double the nm value - 10 percent .

    5 NM to kms,  5x2 is 10 , minus 10 percent ,  19 km

  altitudes in feet , ft ,  1 foot is .3 m ,  3 feet is 1 m

  FL stands flor flight level , is 1 FL is 100 feet.  FL 110 is 11.000 feet,  of 3.300 meters.

   1 knot is 1 NM/hour ,   wind speed is given in knots,  10 knots is roughly 18km/h , double knots to be on the safe side.

  Lift in thermals can be given in ft/min , feet per minute ,   1000 ft/min  is   300 m / 60 seconds what corresponds to 5m/s

American Varios work in ft/min  feet per minute. Also normal aircraft Varios do that.
1000 ft /min  is around 5m/s.  1000ft = 300m ,   300m/60 seconds = 5m/s

 Pressure values

  1 Atmosphere  coresponds to 1013.25 millibars or hectoPascals or 760 mm Hg.

Guess the next lift of a fire

 Winter time in the Highveld.  One can use veldfires as thermals. And you see the smoke of a fire nearby going up.

If the smoke goes up under 45 degree then the rate of clim of that lift and the windspeed is the same.

The windspeed you can figure out from your GPS, comparing the different groundspeeds as you turn.

Example,  your GPS  shows 18 km/h into wind , 54 km/h with the wind . Close, withing glide range is a fire that goes up under 45 degree.
 How good will the expected lift be?

    54-18 =  36 , divide by 2 gives us  a windspeed of 18 km/h

   Which corresponds to 5m/s ,  1m/s is 3.6 km/h.   10m/s would be 36 km/h .

  Your smokre goes up with 5 m/s. If the smoke iwould be flatter then the lift will be less. If it goes up more straight then the lift is better.

   Your glider will have a sink of at least 1m/s, more like 1.5, maybe 2 m/s.
 Therefore one can expect your Vario to show a 3m/s once you get into the smoke.


What is my glide ratio and how far will I get???

 Your GPS will give you the current ground speed in km/h.
 While your Vario will tell you your current sink rate in m/s down.
  You need these 2 numbers. Unfortunately they are not using the same base. One is m/s the other is km/h.

  Lets say your GPS says 36 km/h.  And your Vario gives you 1.31 m/s down.

  1 m/s is the same as 3.6 km/h.   So the ground speed is 10 m/s.
 every second you go 10m forwards and 1.31 m down.  Or you got a glide ratio of 10 / 1.31 = 7.6

 Ok, that was an easy example.

Let's do a more realistic one.
Leaving the thermal I got something like 48 km/h ground speed and 1.8 m/s sink while flying trim speed.

  48 / 4 = 12 + 1.2  = 13.2

   13.2 / 1.8 = 7.odd

 I do not worry really about the decimals. We fly in such inconsistent air that changes all the time.
Important is a rough idea how far we get.

  Other option

   1.8 * 4 = 7.2- .72 = 6.5
 48/6.5 = 7. something.  Glide ratio exact is 7.4. So what?

 Assuming nothing changes for the next few kms, we can now determine how far one can get.

   Take a guess on your altitude above ground (AGL) in meters, and multiply it with your glide ratio.

  Easy example, 1000m AGL x 7.odd = 7 km and some extra meters.  Keep the odd extra as safety altitude to find a decent landing spot.

 Flying best glide  can vary

  In calm air, with no ups and down currents, try to find the best glide of your glider and maintain it.
 But we hardly fly in calm air. When we got lucky to get up and away, then it is due to those thermals going up.
But what goes up must come down somewhere.  So, inevitable, we will encounter sink.
Idea in flying xcountry is to get as far as possible.
Flying too slow in sink will result in wasting altitude.
Flying too fast will increase your speed but also your sink. And the sink will finally grow more than the gain in forward speed.


  You start off with 48 km/h.  48 are around 13.3 Ground Speed and 1.31 m/s sink.
   Lets say this is at trim speed 36 km/h; therefore you already got 12 km/h pushing you.
  I calm air you would have a 10.1 glide. But this is not calm air.
 You are in 3 m/s sink says the Vario.  The 3 m/s consist out of 1.31 m/s sink from you glider and 1.7 m/s sinking air.

 If you do nothing then your glide ratio is now   13.3  / 3  = 4.44
or 3x4 = 12 - 1.2 = 10.8, 48/10.8 = 4. and some little bit

Lets push speedbar, GPS shows 60 km/h, 12 km /h wind from the back, your airspeed is 48 km/h.
 At 48 km/h the polar gives a 2.8 m/s. Add the 1.7 m/s of sinking air   and now you get 4.5 m/s sink

  60 km/h is 36 + 12 + 12 = 16.6 m/s   divided   4.0 m /s  = below 4, in fact 3.7, no good, too fast

  Lets push less speed bar.
  Instead of 60 km/h we only fly with 54 km/h Ground speed according to the GPS.
 Still 12 km/h pushing from the back, what makes it 42 km/h air speed.
 Polar at 42 km/h gives us 1.7 m/s sink plus then 1.7 m/s of air sink and the Vario now shows 3.4 m/s down.

     54 = 36 + 18    = 15 m/s divided by 3.4 = 4.4, slightly better

Speed to Fly

 Besides flying best glide one can do more to squeeze some more performance out of your wing.

This  is called speed to fly.

We got 3 pilots  A B and C. Flying the same Wing.

They are now  under the same cloud at the same altitude leaving at the same in the same direction to head to the next thermal.

Which is 3.6 km away . No wind and no sink around the thermal to make this example easier.

 Pilot A flies best glide , with a 10 m/s, 36 km/h best glide and gets there 6 minutes  or 360 seconds later.

 Lookup in he polar gives us a sink rate of 1.3 m/s for 36 km/h  and  he has lost 360x1.3 =  468m since he left cloud base.

 Pilot B flies a bit faster , 40 km/h or 11.1 m/s ,  324 seconds,  1.5 m/s  ,   arrives  36 seconds earlier than A, but has lost  486m.

 Pilot C flies 44 km/h , 12.2 m/s ,   takes 295 seconds ,  2 m/s , is  65 seconds before A in the thermal and lost 590m

Now it depends how strong that thermal is in average

 By the time Pilot A enters the thermal at a 468m level below cloud base

 With a 1 m/s thermal ,  Pilot C has gained 65 m , is now 590-65 = 525 down,  A is still 57m higher

        B gained 36m , now at 450m, or is 18m above A by now, or 75m above C

   With a 1 m/s the rank is now B-A-C

 If this is a 2 m/s thermal then  C has made 130m good, 460m, or 8m above A

       B gained 72m , 414m, 54m above A,  46m above C

   With a 2 m/s we got B-C-A ,

   If it is a 3 m/s thermal then C has climbed 195m , 395m level, 173m above A

         B has climbed 108m, 376m, 192 m above A , 19 m above C

   At 3 m/s , B-C-A,  with BC and close together. Pilot A trailing behind

Overall  B comes out tops.

 C would probably beat them if they would end up in a 4 m/s average thermal, would I reckon is very rare.

 In average we find 1-2 m/s thermals out there. So add a 1 m/s or 3.6 km/h to your best glide .

  What puts you with an Effect and downwind    back into trim speed, hands up, maybe a little speed bar.

 For those who love Math's, lets put this into formulas

   We got to wings,  A and  B who fly over a certain distance D .

   Forward speed is Vf, Sink of each wing is Vs , glide ratio R for each wing.

   Wing A got  forward speed VfA , sink  VsA , glide ratio RA = VfA/VsA

   For A to cover distance D takes him  the time TA = D/VfA

  In that time he lost the height HA = TA x VsA = VsA * (D/VfA)

  For wing B to cover the Distance D takes B the time TB = D/VfB

   He has the height HB = VsB * TB = VsB * (D/VfB)

Lets say B flew faster than A

 The time difference TAB between A and B to travel the distance D   is  TAB = TA- TB = (D/VfA - D/VfB)

  B arrives TAB earlier than A ,and got time to thermal up in a X m/s thermal .

  He gains  TAB * X meters by the time A arrives.    B will now be at a height loss of  HB - TAB*X

 The height difference between A and B by the time B arrives in the thermal is

  HAB = HA - (HB-TAB*X)

 HAB = VsA*(D/VfA)  -  (VsB*(D/VfB))-X*((D/VfA) - (D/VfB)))

  HAB/D = VsA/VfA - ((VsB/VfB) - X*((1/VfA) - (1/VfB)))

  HAB/D is a height loss to distance traveled ratio ,

  HAB/D = 1/RA - ((1/RB) - X*((1/VfA) - (1/VfB)))