Rethinking the question of sail power

Revised:  7/6/2012        Subject to Revisions

The information regarding wind pressure on flat surfaces indicates that the original 16' tall by 4' wide sail panels for the prototype wind waggon would be insufficient producing less than one horsepower. Consequently, further thoughts suggest that both the turntable diameter and sail height should be increased to develop more power.


 By growing the turntable to 20' diameter and sail panel height to 30' with a width of 8' the wind pressure grows considerably. Further, with the increased diameter, more sail panels can exist. The sail bearings could perhaps be at a diameter of 18'. The bearings would lie in a circle whose circumference is 56.5'. The sail panel bearings lie 2/5ths of the distance from front to back of the sail or 3/5^th of the distance from the back to front. Two adjacent sails must clear their back sections when rotating which indicates a sail spacing of 2x3/5^th or 1-1/5^th or 1.2 times the width of a sail, plus clearance of about 2” or 0.2 of a foot.  Each sail provides half of the clearance or 1” or 1/10^th foot.


Using the rotating clearance for sails as 1-1/5th the sail width and a bearing site diameter of 56.5' a couple of possible sail widths and count occur. With eight sail panels around the spacing of the bearings is 7.0625'. This spacing must represent 1.2 of the panel width which comes to 5.8854'. By deducting 2/10ths of a foot for clearance each sail panel must be 1/10' less or 5.78'. Round this to 5.75' to make the overall dimension more rounded.


With eight panels, four would be capturing wind power at the same time. They would be at angles of 22.5, 67.5, 112.5 and 157.5 degrees. The wind pressure on those panels are proportional to the sine of the angles times the pressure on a 90 degree panel which is (0.38268 + 0.92388) x2 = 2.613. The pressure on a 90 degree full panel of 5.78' x 30' (173.4 sq ft) for a 20 mph wind is 1.6 psf x 173.4 sq ft = 277.44 lbs.  The combined pressure on the four downwind panels would be 724.95 lbs.  The sail panels would be expected to move at about 10% of wind speed which is 0.1 x 88/3 = 2.933 ft/sec.  The turntable would rotate once in 19.26 seconds or 3.1 rpm.  The torque applied to the turntable shaft would be 724.95 lbs x 9' or 6,524.56 ft lbs.  Assuming the turntable shaft has a 1' circumference, in one revolution in 19.26 seconds a force of 6,524.5 lb would be applied or 338.76 ft-lb/second.  This corresponds to about 0.6159 horsepower.  The horsepower increases as the square of the wind velocity.  At a 40 mph wind the horsepower is 2.4636.   It might be a bit more than that as the turntable rotation rate will increase as well by double.   That would further increase the horsepower by a factor of 2 to 4.9247. 

Force on a sail per square foot at sea level is ~ 0.004v^2 where V is wind speed in mph.  A revised concept vehicle was devised for the story that lowered the turntable to a point a few feet above the tops of the wheels and tapered the sail panels to reduce the tipping wind force at the top of the turntable.  A design of that configuration will be pursued using the eight sail panels.

Another option might be to use the original quantity of six sail panels. For that instance adjacent bearings lie 9.4157' on centers. This space must represent nearly 1.2 of a sail panel width which comes to 7.847'. Deducting a bit for clearance and rounding suggests 7.70'.  The sail panel area would be 7.7' x 30' = 231 sq ft.  the wind force on a 90 degree panel would be 369.6 lb.   The panels would be 60 degrees apart.  The downwind side would have one panel at 90 and two at 30 degrees to the wind.  The combined force would be 2 times one panel for a total of 739.2 lbs.   Sail panel rotating speed would be the same as the previous case at 19.26 seconds per revolution.  Turntable torque would be 6,652.8 ft. lbs, about the same as previous. 


Curved sails with airfoil like shapes would increase power somewhat but complicate the design of the sail panels and would further require the use of some form of trim method aligned with the wind.  By doing his however, sails moving with and against the wind can both contribute rotational force to the turntable.  This constitutes a further radical improvement in technology and will be left for perhaps a follow-on model project.