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Old December 19th 20, 10:54 PM posted to rec.aviation.soaring
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Default Arduino Based Soaring Related Devices

OK guys, let's get this sorted out - and Yes, I will have donned my flame-proof suit by the time you're reading this!

A workable figure for the 'underlying' tension, (D + U), can be arrived at as follows: work out ...
D = (total weight of glider + pilot, etc.) / best glide ratio of that glider, and
U = (total weight of glider + pilot, etc.) / 10
Then add D and U to get the total 'underlying' tension (the steady-state tension, if you prefer).

The theory:
Tension in the aerotow rope in flight comprises 3 components:
D: the drag of the towed glider, dependent on its weight and its glide angle at towing speed
U: the "pulling Uphill" force, which is the weight of the glider x the sine of the angle of climb through the air (normally written as sin(angle))
J: the highly unpredictable and dynamically variable Jerk or "impulse" forces, resulting from bumps in the air, wiggles by the tug pilot, and proper (or otherwise) following behaviour of the glider pilot. These will also be scaled by other factors, such as elasticity and mass per unit length of the tow rope and (to a small extent in practical cases) by the respective total masses of tug and glider.

Note for D: normal towing speed is rarely far from best glide speed
Note for U: typical figures, in UK units:
- for a single-seater: 7kts climb at 70kts airspeed, giving the sine as 7/70 = 1/10
- for a two-seater: 6kts climb at 60kts airspeed, giving the sine as 6/60 = 1/10
- for better two-seaters: surprisingly little difference in climb angle, but ...
Note for J: this is potentially so variable that imprecision in assessment of D and U is unlikely to be of any concern.

Of course, a really powerful tug towing a really light glider will climb more steeply, so 10 may not be appropriate as the divisor in U.
If determining the sine in your own case, you must use identical units for airspeed and rate of climb - any density correction you apply to airspeed must also be applied to rate of climb. Some varios may give you true rates of climb, but the ASI will not give you true airspeed!
Note that extra climb rate caused by flying through lift does not affect the geometry, so does not affect the 'underlying' tension. It may well have an effect on variability of J - particularly in gusty thermals.

Martin's explanation was about right, in principle, but wrong in that the 'Uphill' component is significantly larger that the 'Drag' component for any practical glider (as opposed to hang-glider).

Eric wrote "No trigonometry required." But that *is* trigonometry - just without the frightening name!

Some may think that I have been random in my use of "mass" and "weight" - but no, barring slip-ups, and bearing in mind that it's late here!

More detailed explanation could be given, but are you still awake? Do you still have the will to live?
Happy Christmas, J.