Have you ever been faced with the situation when flying head wind and you've hit lift and wondered if its worth stopping to climb in? Well I have.
I have experienced this competing in the two previous WA State Comps and found myself leaving 3 m/s (600 fpm) thermal because I thought I was drifting back too much only to hit the deck. Before the comps this year I decided to sit down and work out the maths for this and came up with some very surprising results.
Assumption for my calculations:
I won't bore you with the maths unless you-d like a copy of my calculations (firstname.lastname@example.org) but I'll provide you with the gist of my thoughts.
1. As I climb in a head wind I'm drifting backwards. As such I have a positive L/D going backwards. The L/D is given by my drift backwards and my climb rate. As long as this L/D backwards is greater than my L/D forward gliding into wind then I will get a net gain along the course line.
2. For various headwind conditions (eg windspeeds which I can calculate from the difference of my GPS ground speeds and my airspeed indicator) the best L/D, airspeed and sink rate can be calculated. The resultant L/D into a headwind is given by solving the intersection of the gliders polar curve (thanks very much Mr Chris Arai) and a straight line passing through the airspeed axis of the polar curve at the corresponding wind speed alue.
3. Once I known my best L/D at certain headwind conditions I can calculate the thermal strength I need to give the positive L/D backwards. The results are as follows:
I have added a percentage onto the climb rates to allow for the fact that it takes time to centre and we all fall out of thermal now and again (sorry Tomas didn't mean to include you in this).
What was surprising to me was how low the climb rate that are required. I had the opportunity to test these figure on the first day of the WA State Comps in 1998.
On the first day of the WA State comps the task was 105 Km from Wylie to Goomalling turn point (60 Km) then on to Northam (45 Km). The last 45 Km were into a 10Km headwind. I reached the turn point at 4.00pm after leaving the paddock at 2.45pm. Just past the turnpoint I was down to 500 m (1500ft) and went through a weak thermal (0.5 m/s - 100fpm). I started circling and drifting backwards at a significant rate. At this point in time I thought twice about gliding forward and hitting the deck or staying with the thermal. However, another pilot joined me so I decided to test my calculations out. The thermal got better peaking at 2 m/s (400fpm) which was 1.5 m/s (300fpm) more than my calculation told me. Sure enough thermal by thermal we got closer to goal finally arriving at 6.30pm. Normally in such a headwind I would not have bothered to circle unless I was going up at least 2 m/s (400fpm) plus.
I know use these figures all the time and have even begun to think they could even be on the conservative side due to the general observation that thermals tends to drift slower than the wind speed. I hope these figures are of use and seek any feedback from other pilots.