The Wrights' "Fourth Flight" - Mensuration

Mensuration  of  the  “Fourth  Flight”

by Joe Bullmer 

( Figure 1)  Photograph identified by Orville Wright as the end of the fourth flight Dec 17, 1903

Measurements

          On December 17th, 1903,  the Wright brothers claimed they made four attempts at manned, powered flight near Kitty Hawk, North Carolina. Piloting was alternated between the brothers with Orville making the first attempt. The first three were basically out of control throughout, none exceeding 200 feet in distance. However, the fourth attempt, the second by Wilbur, was claimed to have gone 852 feet with its mid portion under fairly smooth control. 

         A photograph which Orville Wright asserted in writing was taken after the fourth attempt, shows the launch rail and the aircraft off at a distance. (See Figure 1 above.) Some have questioned whether the aircraft actually appears to be 852 feet, a sixth of a mile, beyond the end of the launch rail. Consequently, an analysis of the photo was done using magnification devices and common geometric and trigonometric mensuration techniques on large scale proportionally accurate prints of this and other relevant Wright photographic plates.

         One of the first things evident in this analysis, particularly on blowups of the photo in question, is that the propellers, and thus the engine of the aircraft, are stopped. Apparently this had not been noted prior to this examination. Also, the aircraft is on or very near the ground.  If indeed this is a photo of a flight, it was definitely taken after the end of it. (Figure 2)

      

(Figure 2) "Fourth Flight" photo blown up, showing one of the stopped propellers highlighted.

     The first step in any mensuration analysis is to identify known dimensions. The launch rail appearing on the right of the photo was known to be 60 feet in length.  The airplane off in the distance had a wing span of 40 feet and four inches with a separation between the biplane wings of 74 inches.  (Due to the small size of the image and its rounded wing tips, for mensuration purposes the wing span used here was 40 feet, an approximation of less than 1%.)  Comparison of the ratios of wing tip separations to span showed the aircraft to be headed within a few degrees of directly away from the camera, its wings essentially crosswise to the camera. (parallel to the optical plane).

         Major unknowns in the subject photo are the focal length of the camera, the distance from the camera to the launch rail, the rail’s angle to the camera, and the size of and distance to the sawhorse appearing in the photo.  Focal length of a camera can often be used to calculate accurate distances to objects of known size. However the bellows type camera used by the Wrights has a variable focal length dependent upon the lens used, so since no record of it was found it was considered unknown for this analysis.  Also, since the camera’s tripod had adjustable legs, it’s height above the ground is not precisely known.

     In mensuration of this type, it is desirable, if possible, to perform independent analyses using horizontal and vertical dimensions for verification or refinement of results.

    Horizontal Mensuration 

         The camera was mounted on a tripod about four feet in height and obviously pointed somewhat downward as evidenced by the optical axis being below the far horizon in the uncropped version of the photograph appearing as Figure 3.

 

(Figure 3)  Uncropped photograph that Orville Wright identified in writing as the end of the 852 feet fourth flight

   

         Subtended angles of objects in the photo as well as the angles between objects were measured from a reference point at the bottom center of a large proportional blowup of the image.These angles were then graphically referenced back ten feet to an assumed camera position.  The distance from the reference point at the bottom of the photo back to the camera position was estimated considering camera format, pointing angle, and footprint sizes appearing at the bottom of the photo.  It will be shown later that, due largely to compensating factors, the exact distance between the camera and reference point is not critical to calculation of the distance from the end of the launch rail to the aircraft. 
  

         Ignoring less than two degrees of parallax, the triangle described by the 60-foot rail and lines from its ends to the camera resulted very nearly in an isosceles triangle lying on the ground.  Bisecting the 26º vertex of this triangle yielded two right triangles 30 feet on their short sides with angles opposite those sides at the camera of 26º/2 = 13º.  (Figure 4)

Figure 4

   Then 30/tan13º = 30/.231 = 130 feet for the distance from the camera to the center of the launch rail.  But the concern here was with the distance of the aircraft from the launch end of the rail, so that end was 130/cos13º = 130/.974 = 133 feet from the camera. The bisector of the 26º angle (the center of the rail) was 28º from a line through the optical axis.  
  

       Mensuration was carried out using these values, namely 40 foot wings separated by 74 inches and a 60 foot launch rail canted at 28º from the optical plane, the launch end of which was 133 feet on the ground from the camera.
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    In a large print of the fourth attempt photo, the launch rail measured 3.75 inches and the wing span .99.  Two thirds of the 60 foot rail equates to the aircraft’s 40 foot wingspan, so the rail measurement was reduced by two thirds to 2.5 inches to represent the aircraft’s wingspan.This measurement was rotated to be perpendicular to the optical axis of the camera (parallel to the optical plane and the aircraft's wings) by dividing it by the cosine28º which is .883.  Thus forty feet of the rail rotated to perpendicular to the optical axis became 2.5/.883 = 2.83 inches.  (Figure 5)

Figure 5

     Objects twice as far look half as big, so the ratio of their measurement scales is proportional to their distances from the camera.  On the blowup the aircraft’s 40 foot wings measured .99 inches and 40 feet of the rail rotated crossways to the camera was  found to be 2.83 inches.  Their scale ratio is then 2.83/.99 = 2.86. The aircraft was thus 2.86 times farther from the camera than was the end of the rail, or 2.86x133 = 380 feet from the camera.

     Unfortunately since the rail end and the aircraft are not on a straight line from the camera their distances could not simply be subtracted to arrive at the distance of the aircraft from the rail.  Consequently a double triangulation had to be used. 

     The camera, rail launch end, and aircraft center formed a triangle whose angle at the camera was 32º with the distance from the camera to the rail's launch end having been found to be 133 feet.  (Figure 6)

Figure 6

     A line was drawn from the rail end perpendicular to the line going from the camera to the aircraft. Thus two right triangles were formed, one with its acute angles at the camera and rail end, and an adjacent one with its acute angles at the rail end and the aircraft.  Both triangles shared the line from the rail end running perpendicular to the camera-to-aircraft line.The length of the shared line was sin32ºx133 = .53x133 = 70.5 feet.

     The length of the line from the camera to the perpendicular line was cos32ºx133 = .848x133 = 113 feet.  Subtracting this from the distance from the camera to the aircraft gave 380 – 113 = 267 feet from the perpendicular line to the aircraft.  Then the angle of the triangle at the aircraft equaled the arctan70.5/267 = 15⅓º.  The hypotenuse of this right triangle was 267/cos15⅓º = 267/.964 = 277 feet which is then the distance of the aircraft from the launch end of the rail.

      A possible uncertainty in this analysis was the distance of the point on the ground shown at the bottom center of the photo from the camera, so the entire analysis was repeated with the distance set at zero.  Since there are a number of offsetting factors in the procedure (primarily angles offsetting distances) the result for distance of the aircraft from the launch end of the rail in this case was 275 feet, a change of less than 1%.  Thus the calculated distance of the aircraft from the rail is essentially independent of the distance assumed from the camera to the reference point at the bottom center of the photo.   

    

Vertical Mensuration

     There are two objects in the fourth flight photograph other than the airplane that show vertical dimensions, the launch rail and a sawhorse.  Unfortunately, the rail height is two orders of magnitude smaller than its length used in the horizontal analysis.  Analyses similar to the horizontal analysis just described but comparing rail heights to aircraft wing vertical separation revealed that an error of one one-hundredth of an inch in measuring the rail height on the blowup of the fourth attempt resulted in an error in calculating the distance from the rail to the aircraft of over 80 feet or about 30%.  The height of the rail near the launch end in the blowup varies from .04 to .06 inches depending upon exactly where it is measured.  Thus it was evident that rail height could not yield a solution comparable in accuracy to that obtained in the horizontal analysis.

   The other vertical dimension that might be compared to the aircraft’s wing separation is the height of the sawhorse.  But there are a number of problems associated with using the sawhorse.  First off, there were at least two sawhorses used by the Wrights at Kitty Hawk.  One appears in a photo from December 14^th of 1903 and another in a photo from May 11^th, 1908.  In both photos sawhorse heights could be scaled from the separation of adjacent aircraft wing tips.  The one from the 1903 photo measured about 21 inches high and the other 28 inches high.

      To calculate the distance from the camera to the sawhorse in the fourth attempt blowup the sawhorse width must be determined.  In both photos mentioned in the previous paragraph the sawhorses were at oblique angles to the optical axis of the photos, and the obliquity angles could not be determined with any accuracy.  Thus although their heights could be measured, the spread of the sawhorse legs could not accurately be determined from these photos.

     In the fourth attempt photo the sawhorse was almost in line with the optical axis and its leg spread is 0.825 of its height.  This ratio could be applied to the known heights of the sawhorses in the other photos to determine their widths, but this left another uncertainty, namely which sawhorse to use.

     A much greater uncertainty arose from the measurement of the subtended angle of the sawhorse legs from the camera in the fourth flight blowup.  Not only was the horizontal subtended angle small (from two to three degrees) but optical parallax becomes a factor.  The vertical parallax angle to the sawhorse would be nearly six degrees, a non-negligible amount.

     (The importance of parallax can be easily seen by looking down one of the acute angles of a 45º or 30º-60º triangle.  Looking straight down on the triangle the true angles are obvious.  But looking at an acute corner with the triangle nearly edge on to the line of sight it becomes evident that even small changes in viewing angles result in big changes in apparent angles of the corner.  In fact, at only small sight angles to the plane of the triangle its acute corners appear as obtuse angles.)

     Determination of the distance from the camera to the sawhorse was crucial in determining its scale factor relative to the scale factor of the aircraft, and thus the distance to the aircraft.  Multiple analyses revealed that an error in the subtended angle of the legs of the sawhorse of ½ degree resulted in an error in calculation of the aircraft distance from the end of the launch rail of over 70 feet.  Considering possible errors introduced from assuming:

      a.  that both sawhorse proportions are the same,

      b. that the subtended angle of the sawhorse legs from the reference point in the blowup can be determined much more accurately than ½ degree, and

      c.  that six degrees of parallax can be neglected,

it was concluded that any aircraft distance derived from the sawhorse could not lend more accuracy to the result obtained from the horizontal analysis that used the launch rail length.

Result

    

     To explore any possible source of significant error, the horizontal analysis was repeated assuming that the camera was positioned 60 feet farther back relative to the launch rail, i.e., 30 feet behind a line on the ground perpendicular to the rail at its starting end. In this case the distance of of the aircraft from the rail's launching end came out to be 298 feet, an increase of 7 1/2 percent.  Consequently, the horizontal analysis is considered accurate to within about 7%.  Both vertical analyses, although encompassing the horizontal result, showed uncertainties of nearly 30%.  So it was evident that vertical analyses could not improve confidence in the result.  Thus the most confident result of the mensuration was obtained from the horizontal mensuration alone.  Therefore the conclusion of this analysis is that

The distance from the launch end of the rail to the aircraft was found to be 277 feet with a confidence of plus or minus 19 feet.

This is less than one third of the 852 foot distance claimed for the fourth attempt at Kitty Hawk on December 17^th, 1903.  Even the most distant results from the low confidence vertical analyses were well under half of the claimed distance.  In order for this analysis to yield the distance claimed, the rail would have to have been 200 feet long and 450 feet from the camera and this analysis would have to be in error by 210%.  Conversely, if it was 852 feet away from the end of the 60-foot rail, the aircraft's image would have to appear one-third of its present size.

Implications

     The photo claimed to be of the fourth attempt on December 17^th, 1903, at Kitty Hawk and examined here clearly shows that the propellers were stopped and the aircraft was on, or very near, the ground.  So, based on this analysis, either the aircraft did not go anywhere near 852 feet, or if it did, this is not a picture of it.

     In a November 2^nd, 1906, letter* to Octave Chanute, Wilbur Wright stated their opinion that any flight of less than 100 meters, 328 feet, would just be a "jump" and would prove, using his word, “nothing.” Here he was discussing distances over the ground and considering the requirement to achieve sufficiently stable control to demonstrate the thrust necessary to maintain flying speed and generation of enough lift to sustain the vehicle in the air as opposed to merely making a semi-ballistic hop using the kinetic energy obtained from a ground run.  None of the other attempts earlier that day exceeded 200 feet.  Consequently, this analysis indicates that, if held to their own criterion for success, the Wrights' photography provides no evidence of a successful powered flight in 1903.

Addendum

      To justify his first attempt on December 17^th as being a success, Orville claimed that without the strong headwind he would have flown over 500 feet.  Some might find it tempting to use this rationale to legitimize their claim for distance on the fourth attempt.  However, to Orville an even more important and often repeated claim was that their aircraft took off using “its own power alone with no assistance from gravity or any other motive source whatever.”

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     In fact the strong headwinds on the 17^th supplied 80% of the lift required for his and their subsequent takeoffs.  Without those strong headwinds there would have been no flying at all by the Wrights in 1903.  Their aircraft was almost flying sitting still.  So either it flew a great deal farther through the air but could come nowhere near lifting off of the ground on its own, or the plane left the ground on its own but did not demonstrate sustained flight.  It can’t be claimed that the wind had nothing to do with its ability to achieve flight but everything to do with it demonstrating successful flight distances.  Historians can’t have it both ways, and neither could Orville Wright.

     The result of this analysis also calls into question the claimed 59 second duration of the fourth attempt.  Dividing 59 seconds into 277 feet yields an average ground speed of only 4.7 feet per second, or about three miles per hour.  The official government records of the sustained wind speeds at Kitty Hawk on December 17^th as recounted by Orville Wright were 24 miles per hour at the time of their fourth trial and 27 miles per hour during the first attempt.  So the average airspeed for a 59-second, 277-foot fourth attempt would have been 27 miles per hour, the same as the minimum wind speed at the time of their first trial.  In other words, if on that day the wind was so strong that they needed 59 seconds on the fourth attempt to cover 277 feet, then with the stronger wind on their first attempt giving the same airspeed, their vehicle would have taken off on its first trial with no ground run at all and would have made no forward progress whatsoever. Obviously, a 59 second flight time is not compatible with the flight distance calculated herein.

     Assuming an average airspeed for their vehicle of 35 miles per hour on their fourth attempt, and a corresponding ground speed of 11 miles per hour (16 feet per second), it would have taken about 17 seconds to cover 277 feet. If the airspeed was 30 miles per hour, the flight time would have been 31.5 seconds. Headwind gusts would have increased these flight times slightly.

(Figure 7)  Photograph clearly showing three objects on lower wing. Again, this is the photo claimed by Orville Wright and historians to document the fourth flight, December 17, 1903. (blown up and cropped) **

     This analysis can offer no further insight into the significant discrepancies between the times and distances claimed for the fourth flight attempt at Kitty Hawk on December 17th, 1903 and those calculated herein from the photograph claimed to show the end of the fourth attempt.  It also does not address the three dark objects on the lower wing of the aircraft. (Figure 7 above.)

 *  This article is a companion piece to the previous study in this blog by Joe Bullmer titled: Kitty Hawk - 1903 - What Happened?  
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Copyright 2019 - Joe Bullmer
 

Aeronautical engineer, historian, and author, Joe Bullmer

"The WRight Story" available at Amazon.com.

**Note: Photos and their captions provided for the most part by the editor of "Truth in Aviation History."