In two letters sent to Dr. G. A. Spratt (an aviation enthusiast), Wilbur Wright reported the progress he and his brother had made, up to September 10, 1904, regarding Flyer II, a plane powered by a 16-17 hp engine. (The pilot had no means to control the motor in flight. He could just stop it, in which case the machine landed.)
The plane needed an airspeed of about 30 mph to fly well. The machine lifted at 23-24 mph (airspeed) but it always fell unless the airspeed reached 25 mph. Between 25 and 30 mph it struggled to keep flying but if somehow reached 30 mph then it accelerated without problem, by itself, to 45 mph.
Assuming the aerodynamic resistance was $$\text{Drag} = kV^2$$ where k is a constant and V was the airspeed, it results that the plane needed the power $$P = \text{Drag} \times V = kV^3$$ to fly at a constant speed, V, and in consequence the necessary power for 45 mph would have been $(45/30)^3 = 3.375$ times greater than that required for flying at 30 mph. In other words, the apparatus would have needed at least 3.375 x 16 hp = 54 hp to reach 45 mph. The difference in power is enormous.
Between 30 and 45 mph the drag should have followed a significantly different law from $\text{Drag} = kV^2$. What would that law be?
1904-08-16, Wilbur Wright, “Letter to G. A. Spratt”, Dayton, August 16, 1904.
Dear Dr. Spratt, ...
Up to Aug. 1st we had made but fourteen trials; since then we have made seventeen more. So far our longest flight is only 1304 ft. in 39-1/2 seconds, which though farther over the ground than our longest flight at Kitty Hawk is not its equal in duration of time or distance through the air. We are however working under much less favorable conditions so far as grounds and atmospheric conditions are concerned. We have found difficulty in getting satisfactory starts owing to the fact that the winds are usually very light by spells, and the new machine requires a higher relative speed for starting than the old one. It lifts at a speed of 23 or 24 miles an hour but the angle is so great that the resistance exceeds the thrust and the machine soon stalls. Between 25 and 30 miles it is a case of nip and tuck between them; but after the relative speed reaches 30 miles, the thrust exceeds the resistance and the speed accelerates till a velocity of forty five or fifty miles is reached. So far the highest speed attained is forty five miles, but it may exceed this when we get to making longer flights. We are proceeding very cautiously; and do not intend to attempt anything spectacular until we know that it is safe, and we know all of the machines peculiar tricks. ... Yours truly, Wilbur Wright.
1904-09-10, Wilbur Wright, “Letter to G. A. Spratt”, Dayton, September 10, 1904.
Dear Dr. Spratt, ... We have made forty five starts with our 1904 Flyer. Unless the relative speed at starting is 27 miles in a calm and two or three miles more than that in a wind, the machine will gradually slow down till unable to fly. After the relative speed passes thirty miles the velocity accelerates till a relative speed of 45 to fifty miles is reached. We found it difficult in practice to get a speed down the track greater than 20 miles an hour, so that unless we had a wind of about 10 miles we were not sure of being able to fly for a lull in the wind would let us drop below the real flying limit. As we were not ready to turn our backs to such a wind on account of the enormous speed in landing when going with the wind our flights have been confined to the length of our pasture field. We have made a number of flights between 1250 and 1450 ft long. We have now finished a starting apparatus which gives a speed at start of 27 miles an hour in a dead calm, and expect shortly to begin circling. With longer flights and less hauling the machine back, we hope to get more practice than heretofore. With kind regards, Yours truly, Wilbur Wright.
This is just an illustration that shows Flyer I and II. It has nothing to do with the two letters quoted above.
The 1904 Wright Flyer II was almost identical to the 1903 Flyer, as you can see by comparing these two photos. The picture with Flyer I (1903) was first published in “The Wright Brothers’ Aeroplane”, The Century Magazine, New York, September 1908, Vol. LXXVI, No. 5, pp. 641-650. The one with Flyer II (1904) later.