Something strange regarding the 1904 plane (Flyer No 2) built by the Wright Brothers
I am looking for an as simple as possible mathematical model that can explain how it really worked.
In 1904, the Wright Brothers started to test a new plane, Flyer II, somewhere near Dayton, Ohio where they managed to get permission to use a flat pasture for their experiments.
The winds were light there and, in the beginning, they had no catapult to quickly accelerate their machine and throw it into the air. They simply started the engine of the airplane which began to move along a track (a runway) while a headwind of moderate intensity was blowing and finally they got into the air and flew.
What is not quite clear (read the attached letter) is how exactly the plane took off.
W. Wright says that Flyer II lifted at 23 mph but he adds that Thrust got greater than Drag (Resistance) at 27 - 28 mph.
How could the plane accelerate from zero to the take off velocity if Thrust was less than Drag at speeds below 27 - 28 mph?
I made an attempt to write the equation of Flyer II as it accelerated along the track (see 1 and 2) but it is quite clear that the airplan speed gets negative unless Vw > 27 or 28 mph and such a wind speed was not available near Dayton.
1) T(Vp+Vw) - Kd * (Vp + Vw)^2 = m * dVp/dt (Thrust - Drag = ma)
2) m * g = N + Kl * (Vp + Vw)^2 (Weight = Normal reaction of the track + Lift)
where:
m = plane mass
Kd, Kl = drag and lift constants
Vp = plane speed relative to the ground
Vw = wind speed relative to the ground
g = 9.81 m/s^2
N = the normal reaction of the runway (track)
Can somebody on the forum correct my equations to make them agree with the description of W. Wright?
Fragment from a letter written by Wilbur Wright to Octave Chanute, on August 8, 1904:
"One of the Saturday flights reached 600 ft. ...
We have found great difficulty in getting sufficient initial velocity to get real starts.
While the new machine lifts at a speed of about 23 miles, it is only after the speed reaches 27 or 28 miles that the resistance falls below the thrust. We have found it practically impossible to reach a higher speed than about 24 miles on a track of available length, and as the winds are mostly very light, and full of lulls in which the speed falls to almost nothing, we often find the relative velocity below the limit and are unable to proceed. ... It is evident that we will have to build a starting device that will render us independent of wind."
For the original hand written letter see: (Library of Congress,
Page 52 of Octave Chanute Papers: Special Correspondence--Wright Brothers, 1904)
I am looking for an as simple as possible mathematical model that can explain how it really worked.
In 1904, the Wright Brothers started to test a new plane, Flyer II, somewhere near Dayton, Ohio where they managed to get permission to use a flat pasture for their experiments.
The winds were light there and, in the beginning, they had no catapult to quickly accelerate their machine and throw it into the air. They simply started the engine of the airplane which began to move along a track (a runway) while a headwind of moderate intensity was blowing and finally they got into the air and flew.
What is not quite clear (read the attached letter) is how exactly the plane took off.
W. Wright says that Flyer II lifted at 23 mph but he adds that Thrust got greater than Drag (Resistance) at 27 - 28 mph.
How could the plane accelerate from zero to the take off velocity if Thrust was less than Drag at speeds below 27 - 28 mph?
I made an attempt to write the equation of Flyer II as it accelerated along the track (see 1 and 2) but it is quite clear that the airplan speed gets negative unless Vw > 27 or 28 mph and such a wind speed was not available near Dayton.
1) T(Vp+Vw) - Kd * (Vp + Vw)^2 = m * dVp/dt (Thrust - Drag = ma)
2) m * g = N + Kl * (Vp + Vw)^2 (Weight = Normal reaction of the track + Lift)
where:
m = plane mass
Kd, Kl = drag and lift constants
Vp = plane speed relative to the ground
Vw = wind speed relative to the ground
g = 9.81 m/s^2
N = the normal reaction of the runway (track)
Can somebody on the forum correct my equations to make them agree with the description of W. Wright?
Fragment from a letter written by Wilbur Wright to Octave Chanute, on August 8, 1904:
"One of the Saturday flights reached 600 ft. ...
We have found great difficulty in getting sufficient initial velocity to get real starts.
While the new machine lifts at a speed of about 23 miles, it is only after the speed reaches 27 or 28 miles that the resistance falls below the thrust. We have found it practically impossible to reach a higher speed than about 24 miles on a track of available length, and as the winds are mostly very light, and full of lulls in which the speed falls to almost nothing, we often find the relative velocity below the limit and are unable to proceed. ... It is evident that we will have to build a starting device that will render us independent of wind."
For the original hand written letter see: (Library of Congress,
Page 52 of Octave Chanute Papers: Special Correspondence--Wright Brothers, 1904)
