JUNE II, 1914] 
NATURE 389 
model of the aeroplane or the part of the aeroplane 
the behaviour of which it is desired to study, is sup- 
ported on the arm of a balance by means of which 
forces and moments acting on it, when a current of 
air is produced in the channel by a suitable fan, can 
be measured. The velocity of the air current is 
measured by a Pitot tube, and a constant distribution 
of velocity across nearly the whole of any section of 
the channel is secured by special arrangements. At 
the National Physical Laboratory there are now two 
channels, one 3 ft. square and the other 4 ft. square, 
in daily work. A third channel, 7 ft. square, is 
nearly complete. The results of lift and drift experi- 
ments on the same aerofoil, when measured by 
different observers in the two channels recently, were 
found to be practically identical. 
As to the means of stepping from the model to the 
full-scale aeroplane—the force on a surface due to the 
wind may be written as KSV*, where S is the area 
of the surface, V the speed of the wind, and K a 
quantity which for two similar surfaces similarly 
placed is approximately a constant, independent, that 
is, of the velocity and the area. Experiment proves 
that the force is not strictly proportional to the square 
of the speed. Curves are given in the paper showing 
that as a result of determinations of the lift and drift 
coefficients for an saerofoil at speeds changing from 
10 to 50 ft. per sec., it appears there is a growth in 
the coefficients as the speed increases. Lord Rayleigh 
has pointed out that if K be not constant for similar 
surfaces it must be expressible as a function of VL/v, 
where V is the velocity of the current, L some linear 
dimension of the surface, and v the kinematic viscosity 
of the air. From experiments on model and full-sized 
aerofoils, it appears that at the highest value of VL 
yet reached in the model experiments the value of the 
lift/drift ratio is somewhat less than for the full-scale 
experiments, but that values for the coefficients found 
from the 50 ft. per sec. observations in the channel 
do not differ greatly from those belonging to the actual 
machine. This point will be checked more fully when 
the large wind channel is complete. 
A method of checking the accuracy of the model 
work is to calculate the forces on an aerofoil from the 
pressure distribution. This has been done at the 
N.P.L., and in the case of the lift the agreement is 
complete; in the case of the drift the calculated results 
are too low, which is to be expected, as in the calcula- 
tions, air friction on the surface is neglected. Refer- 
ence is made to the fact that in designing a wing, the 
shape of the upper surface is more important than the 
lower. 
The results are given of measurements made on a 
model of a monoplane of ordinary type, of the forces 
and moments produced in the plane of symmetry when 
the attitude of the machine changes, but without 
yawing; and the forces and moments produced by 
yawing without alteration of the angle of pitch, so 
that flight is horizontal. Curves are also given of the 
pitching moment of a biplane model for various set- 
tings of the elevator. As the result of experiments 
of this kind it appears that the wash from the main 
planes reduces the moment on the tail very greatly. 
The curves given show that on comparing the moment 
about the C.G. of the machine as calculated from a 
knowledge of the shape and position of the tail, the 
elevators being at a small positive angle, with the 
measured moment, the latter is of only half the cal- 
culated amount. Further study is being made to 
determine the best position for the tail. 
Mathematical Investigation into the Stability of an 
Aeroplane.—Mr. Bairstow and Mr. Nayler, of the 
National Physical Laboratory, have recently deter- 
mined the coefficients for the monoplane model pre- 
viously mentioned, and used them to determine its 
NO. 2328, VOL. 93] 
motion in a variety of circumstances, and some 
account of their results is given. The effect of a single 
horizontal gust in the direction of motion is first taken. 
The results of the calculations are given in curves 
which show that the particular machine when struck 
by a horizontal gust loses longitudinal speed at first, 
and after passing through a series of changes of 
velocity, settles down after a few oscillations in less 
than a minute to its original speed relative to the 
wind. The initial loss of speed is accompanied by an 
increase of normal velocity; the machine rises for a 
fraction of a second, acquiring a rapid positive angular 
velocity, but these motions soon change sign and die 
away like the horizontal velocity. The nose of the 
machine rises for 5 sec., at first rapidly, then more 
slowly, and the pitching oscillation thus started dies 
down in the same manner as the others, the motion 
being stable. 
The effect of a single downward gust in the plane 
of symmetry is next described. The curves show that 
relatively to the air the machine acquires an upward 
velocity which dies down in about one second and is 
followed by the slow oscillations as before. The 
changes in the other quantities are shown in the 
curves, and the motion of the machine can be traced 
as before. By combining the results, the effect can be 
found of a change in the direction of the wind or an 
alteration in the propeller thrust or thé position of 
the elevators. 
Two cases of lateral disturbance are next considered. 
This motion in the particular machine dealt with is 
unstable. Curves are given showing the effect of a 
side-wind striking the machine on the left-hand side. 
The machine quickly picks up the velocity of the wind 
After about 7 sec. the relative sideways motion 
is very small, but it gradually increases, and after 
40 séc:( has. reached. some’) 9 ‘per ‘cent. “of the 
original disturbance. Unless the controls are altered 
the side-slipping will continue to increase. A large 
angular velocity of roll is started almost immediately 
and at first this gradually dies down, but after 6 sec. 
or so the divergence term begins to tell and the rolling 
increases unless checked by the pilot. The velocity of 
yaw is at first negative, the machine yaws to the left, 
a motion opposite to that which corresponds to the 
bank. After a time this is reversed, and the yaw and 
bank increase together. 
In another series of curves is recorded the effect 
of sudden banking. After 40 sec. the angle of bank- 
ing exceeds its original value by 63 per cent., while 
the velocity of yaw also increases rapidly, as does the 
side-slipping velocity, which takes place in the nega- 
tive direction. Thus the machine turns to the right, 
increasing the angle of banking, and_ side-slipping 
inwards and downwards at the same time. 
In the descriptions above it has been assumed that 
the controls are not touched, but a comparison of 
the curves referred to above with the curve obtained 
when the effect of warping or of turning the rudder 
are considered, shows that the control of such an 
unstable machine is not easy. 
Messrs. Bairstow and Nayler have in this way 
solved the following problems :—An aeroplane is in 
flight in the air. (1) At a given instant the wind 
changes either in speed or direction, or both, and 
the new conditions remain for a time steady. The 
motion of the aereplane is determined by the curves 
given in the paper: (2) at a given instant the controls 
of the aeroplane are altered. The ensuing motion is 
defined by other curves: and (3) by a suitable com- 
bination of the curves the effect of change of wind 
and change of control occurring simultaneously can 
be determined. 
If the motion of an aeroplane when moving through 
successive gusts is analysed for a few minutes it can 
