# I calculated that Flyer I and II (1903-04) of the Wright brothers were underpowered. Are there better (drag, lift) coefficients than those of Culick?

Based on what the Wright brothers said in a few letters and two article (all relevant excerpts have been attached to this post), and also using the experimental data in the study "AERODYNAMICS, STABILITY AND CONTROL OF THE 1903 WRIGHT FLYER - Fig. 12 Lift and Drag of the 1903 Flyer" by Fred Culick (1984), I reached the conclusions that both Flyer I and II were grossly underpowered and could not have reached the airspeeds claimed by the Wright brothers. Are there better works than Culick's with more precise drag and lift coefficients?

These are my calculations:

Fragments, from letters and articles of the Wrights, relevant for the question:

1904-03-14, W. Wright, “Letter to O. Chanute”, Dayton, March 14, 1904 “We are hard at work getting ready for Spring. The new machines will be of the same size as the old one but will weigh a little more, 800 lbs. probably. By gearing the engine to run a little faster we will not only carry the additional weight but will have enough surplus to increase the speed to about 40 miles an hour.”

1904-05-20, W. Wright, “Letter to O. Chanute”, Dayton, May 20, 1904. “Our indoor tests of the machinery show excellent results. With the same screws we used last year we get an increase in speed of 50 turns per minute, indicating an increase in power of more than one half. This is partly due to gearing the engine to run at higher speed per turn of screw, and partly to increase in efficiency of the engine itself.”

1904-06-14, W. Wright, “Letter to O. Chanute”, Dayton, June 14, 1904, 1 page. “This machine is entirely new, including engine and machinery. We are using the old screws.”

1904-12-21, Orville Wright, “Letter to Carl Dienstbach”, December 21, 1904, 2 pages. “The two longest flights of the season were made on the 9th of November and the 1st of December. In each of these flights we made almost four complete circles and covered a distance of a little over four and one half kilometers, at a speed of about 35 miles an hour. In the flight of November 9th a weight of 50 lbs. (iron bars) were carried in addition to the weight of the operator; in the flight of December 1st, 70 lbs.”

1907, Wilbur and Orville Wright, “The Relations of Weight, Speed, and Power of Flyers”, Navigating the Air - A Scientific Statement of the Progress of Aëronautical Science up to the Present Time - By the Aero Club of America, London, Heinemann, 1907, Printed in New York, U.S.A., pp. 6-12. “THE flyer of 1903 carried a four-cylinder gasolene motor of four-inch bore and four-inch stroke. Complete with magneto, radiators, tanks, water, fuel, etc., the motor weighed a little over 200 lbs.; and at 1200 revolutions per minute, developed 16 horse-power for the first 15 seconds after starting. After a minute or two the power did not exceed 13 to 14 horse-power. At 1020 revolutions per minute — the speed of the motor in the flights at Kitty Hawk on the 17th of December, 1903, — it developed about 12 horse-power. The flyer of 1904 was equipped with a motor similar to the first, but of 1/8 inch larger bore. This engine at 1500 revolutions per minute developed 24 horse-power for the first 15 seconds, but only 16 to 17 horse-power after a few minutes’ run. Complete with water, fuel, and other accessories, it weighed 240 lbs. The same engine, with a few modifications in the oiling device and the carbureter, was used in all the flights of 1905. A test of its power made soon after the flights of October, 1905, revealed a gain of 3 horse-power over tests made just before mounting it on the flyer in 1904. This gain is attributed to the increased smoothness of the cylinders and pistons produced by wear. The small output of these engines was due to lack of experience in building gasolene motors. … A comparison of the flyers of 1903, 1904, and 1905 shows some interesting facts. The flyer of 1903 weighed, complete with operator, 745 lbs. Its longest flight was of 59 seconds’ duration with a speed of 30 miles an hour and an expenditure of 12 horse-power. The flyer of 1904 weighed about 900 lbs., including a load of 70 lbs. in iron bars. A speed of more than 34 miles an hour was maintained for a distance of 3 miles with an expenditure of 17 horse-power. The flyer of 1905 weighed, including load, 925 lbs. With an expenditure of 19 to 20 horse-power it traveled over 24 miles at a speed of more than 38 miles an hour. The flights of 1904 and 1905 would have been slightly faster had they been made in a straight line, as were those of 1903. In 1903, 62 lbs. per horse-power were carried at a speed of 30 miles an hour; in 1904, 53 lbs. at 34 miles an hour; and in 1905, 46 lbs. at 38 miles an hour. It will be noticed that the weight carried per horse-power is almost exactly in inverse ratio to the speed, as theory demands — the higher the speed, the smaller the weight carried per horse-power. Since flyers can be built with approximately the same dynamic efficiency for all speeds up to 60 miles an hour, a flyer designed to carry a total weight of 745 lbs. at 20 miles an hour would require only 8 horse-power, or two-thirds of the power necessary for 30 miles an hour. At 60 miles 24 horse-power would be necessary — twice that required to carry the same weight at 30 miles an hour. At 120 miles an hour 60 to 75 horse-power would probably be necessary, and the weight carried per horse-power would be only 10 or 12 lbs. At such high speed the resistance of the operator's body and the engine is a formidable factor, consuming 64 times as much horse-power as at 30 miles an hour. At speeds below 60 miles an hour this resistance is almost negligible.”

1908-09, Orville and Wilbur Wright, “The Wright Brothers’ Aeroplane”, The Century Magazine, New York, September 1908, Vol. LXXVI, No. 5, pp. 641-650 (pp. 648-649). “Our first propellers, built entirely from calculation, gave in useful work 66 per cent of the power expended. This was about one third more than had been secured by Maxim or Langley.”

Flyer I, Kitty Hawk, North Carolina, December 17, 1903.

• The Wright flyers at Kitty Hawk may have been helped a bit by rising airflow from the sea breeze against the dunes. No doubt they were marginally powered, noting that an increase in AOA from 5 to 10 degrees could more than double the drag coefficient. One can see how slightly higher airspeed (lower AOA for the same lift) was an advantage. Little wonder they designed their planes to "belly flop" when they "stalled". See Gustave Whitehead, another early pioneer. – Robert DiGiovanni Oct 11 '20 at 13:58
• I think the Wrights made a big point of making sure the powered flights were on flat ground; I don't think they benefited from slope lift. – quiet flyer Oct 11 '20 at 16:46
• "The 1903 plane was considerably overpowered if we are to trust the results of the article I quoted." -- did mean to write "underpowered"? – quiet flyer Oct 11 '20 at 16:49
• @quietflyer, You quoted a text written by somebody else, in his answer. He concluded, based on the data he found, that Flyer I was overpowered. – klausweber Oct 11 '20 at 17:30

The results of a trial made on November 21, 1903, do not match the 1999 wind tunnel measurements. The discrepancy is enormous. The Wright brothers and the people at NASA tested very different planes and propellers otherwise the reported experimental data would have matched well.

I do not agree the 1999 experiments, on the full size model of the 1903 plane, gave more precise measurements than the ones obtained by Fred Culick and reported in 1984.

In the wind tunnel, the reproduced propeller fell short of T=D @ 28 mph test condition when operating at the maximum permitted speed of 340 RPM. These data are being analyzed

The same presentation, at page 10, contains a measurement for $$RPM=340$$ showing $$C_D=0.035$$ and $$C_L=0.66$$ (I extracted these precise values from the diagram using a special software tool).

The minimum drag at 28 mph should have been: $$D=W\frac{C_D}{C_L}=745lbf\frac{0.035}{0.66}=39.50lbf,\space(V_{air}=28mph, RPM=340)$$
$$P_{340RPM, \space28mph}=\frac{V_{air}D}{\eta}=4.47hp, \space \eta=0.66$$ From Orville Wright's 1903 Notebook:

Saturday, Nov. 21 After many attempts to fasten sprockets we finally succeeded by filling threads with tire cement. The engine ran very irregularly, jerking the chains, and shaking the machine terribly. We discovered the trouble lay in the gasoline feed, and after fixing valve so that the vibration could not change it we had no further trouble from that source. The first test of speed was 306 rev. screw to minute (309 in 60½ sec). One cylinder made only a few explosions during the test. On the next trial we got 333 rev. in 60 sec. After dinner we arranged to measure the thrust by supporting center skids on rollers and fastening one end of machine, while we attached a rope to the other end, which ran over a pulley and carried a 50 lb. box of sand. Besides lifting the sand we got an additional pull of 16 to 18 lbs on the scales, which made the total thrust of the screws 132 to 136 lbs, at a speed of 350 revolutions per min. Our confidence in the success of the machine is now greater than ever before. Weather today was warm and pleasant with 6 to 8 meter wind from North East.

Orville Wright says that in a wind of $$6$$ to $$8 m/s$$ (I will take $$V_{air}$$=$$7 m/s = 15.69 mph$$ on average), at $$RPM=350$$, the Wrights got the thrust: $$T = 132 \space to \space 136 lbf, \space (V_{air}=15.69mph, RPM=350)$$ It is true , there is a difference of $$10 RPM$$ between the test described by Orville and that made in the wind tunnel but this can not explain the enormous difference between the thrust obtained by the Wright brothers $$T_{min}=132lbf$$, which would have further increased at $$V_{air}=28mph$$, and that of the group of experimenters, at the NASA facility, which was evidently $$T<39.50lbf$$.

• Only $P=4.47hp$ to fly a $745lb$ plane at $28mph$ seems unrealistic. – klausweber Oct 12 '20 at 13:49

The Wilmington Messenger, Wilmington, North Carolina, May 26, 1904, col. 1, p. 6.

Elizabeth City Economist: A gentleman visiting this city whose home is in Kitty Hawk, is responsible for the assertion that the Wright brothers, of airship fame, will return to Kitty Hawk in the near future and resume work on their aerial monster. According to this gentleman the airship has never been removed from Kitty Hawk and nearly all the interviews published in the papers of Norfolk have been erroneous in this respect. This gentleman has assisted the Wrights in all their work and has a general supervision of their property during their absence. He says that they have not completed the ship and that they will return some time within the next month and resume their work. A story is current that they will complete the ship and make the trip from here to St. Louis sometime this fall.

The text was published (what a coincidence!) in the very day, May 26, 1904, when the Wright brothers flew Flyer II, near Dayton, for the first time. The article says that according to a man that worked for them and took care of their things left behind at Kitty Hawk, the two inventors hadn't finished Flyer I. In conclusion, this machine did not fly on December 17, 1903!

2. Coming back to the question, yes, there are better experimental data than Fred Culick's. They can be found in the article: "Full-Scale 1903 Wright Flyer Wind Tunnel Test Results From the NASA Ames Research Center", from which I extracted the following diagrams:

As can be seen in the diagrams above, for 300 RPM, if $$C_D=0.06$$ then $$C_L=0.7$$, and using the formulas given in the question, it results that the power needed by Flyer I, on December 17, 1903, was only $$P_{300}=7.74 hp$$, which is ridiculously low. For 340 RPM, at $$C_D=0.04$$ ($$C_L=0.7$$), the necessary power would have been just $$P_{340}=5.16 hp$$.

The 1903 plane was considerably overpowered if we are to trust the results of the article I quoted.

(The weight of the plane was taken as $$W=745lbf$$, speed $$V=30mph$$, propellers' efficiency $$0.66$$)

As a note: All experimental tests with models of various sizes, representing Flyer I, have as their primary source of data the 1916 replica built by Orville Wright, not the 1903 original.

• Robert the Reynolds numbers of the models were slightly lower than the "real" Flyers which were around 1 to 2 million at 20-40 mph (9-18 m/s with a 2 meter chord). This is right in the range (from polars) where higher Reynolds numbers will give much more favorable Cl/CD ratios, especially at lower angles of attack. The Wrights work from kite flying and wind tunnels really paid off, albeit just barely. – Robert DiGiovanni Oct 11 '20 at 15:02
• Yes, the prop airflow did help. – Robert DiGiovanni Oct 11 '20 at 15:04
• "In conclusion, this machine did not fly on December 17, 1903" --!! – quiet flyer Oct 11 '20 at 16:44
• Fred Culick measurements and those of AIAA group agree for the case when the propellers did not run: "Comparisons (props-off) with previous wind tunnel tests of smaller models showed fairly close agreement" (see: wrightflyer.org/wp-content/uploads/2012/10/… page 16). – Simplex11 Oct 12 '20 at 0:05