# What is the incidence angle of a propeller in the terminology of the Wright Brothers and how did they obtain it?

What is the angle of incidence of a propeller in the terminology of the Wright Brothers and how did they obtain it?

In Feb. 1903 (see Screw Test 1903, page 8), using a 0.58 hp engine, the Wright brothers tested a propeller characterized by:

Diameter, D = 8.5 ft

Pitch = 15 deg

Surface, $S = 2\ ft^2$

RPM = 245

They measured what appears to be the static thrust and got:

Thrust = 18.75 lbf

Based on the assumption that the propeller can be modeled by a wing (Pitch = 15 deg, Surface = $2\ ft^2$, Lift = 18.75 lbf) having its entire area concentrated in a single point (called the Center of Pressure, C.P.) traveling at RPM = 245 on a circle with the diameter 0.824 x D, $V_{wing} = RPM \times \pi \times 0.824 \times D$, the Wright brothers evaluated its Drag and from Lift, Drag and Pitch using trigonometric relations they obtained the Normal (perpendicular to the chord) and Axial or Tangential (along the chord) components of Lift + Drag (the resultant force) and some angles related to them.

Now comes something I do not quite understand.

The two brothers calculated a reference force defined as:

Total Normal = $k \times S \times V_{wing}^2$ = 24.8 lbf,

where

$V_{wing} = RPM \times \pi \times 0.824 \times D = 61\ \mathrm{mph}$

$k =$ Smeaton’s coefficient $= 0.0033\ \mathrm{lbf} \cdot \mathrm{ft}^{-2} \cdot \mathrm{mph}^{-2}$

Further, the Wrights divided the Lift by the Total Normal

$\frac{\mathrm{Lift}}{\mathrm{Total\ Normal}} = 0.756$

and from this 0.756 they drew the conclusion that the angle of incidence is 7¼ deg. The question is why? What is this angle of incidence and how can it be calculated?

Update

The correspondence between the percentage 0.756 and the angle of incidence, 7¼, comes likely from a table like this (which is for a slightly different wing curvature):

Percentage of air pressure at various angles of incidence

However, as the propeller did not move, the incidence angle of its equivalent wing appears to be identical with the pitch of the same wing and they are not. Why?

• If a wing (a small helicopter blade) rotates about the axis of a stationary motor, how do you define the pitch and incidence angle? This is the question. It appears that Pitch = angle (chord, plane of rotation), AoA = angle(chord, relative wind) = angle (chord, plane of rotation) as the relative wind speed is in the plane of rotation. It seems that, for the Feb 1903 test, Pitch = AoA also called incidence. – Robert Werner Oct 16 '15 at 9:08
• Possible W. Wright, based on the speed of the air blown back by the propeller, believed he was in the equivalent case of a propeller moving forward, a situation when AoA is different from Pitch and this is the reason he did not see a contradiction when he obtained an angle of incidence different from Pitch. – Robert Werner Oct 16 '15 at 17:21

According to various scholars, the Wright brothers were referring to "angle of attack" when they used the term "incidence." They actually published an article by the same title, so the fact is well-established.

References include the following:

In Wilbur's time, the "angle of incidence" was what we now call the "angle of attack" -- the angle at which the wing of an airplane meets the wind (wright-brothers.org).

and

In the Wright's own words: "The lift is thus balanced against the normal pressure on the resistance surfaces ... Therefore, the lift ... at the given angle of incidence (angle of attack) is to the pressure on a square plane of equal area at 90° as the sine of the (...)

The angle of attack of a propeller is defined in various ways, a summary of which is here.

The angle at which this air (relative wind) strikes the propeller blade is its angle of attack.