254 
NATURE 
[May 9, 19f2 
rapidly degraded that after travelling a short distance 
they are merely recognisable as slight variations in 
the direction of the general current. 
The abstraction of wake water by eddy-making 
continues, however, even for very small values of a, 
and has the effect of deflecting the upper boundary 
of the wake as shown. 
The deflection may be considered from another 
point of view as the outcome of the defective pressure 
on the down-stream surface of the plane. 
This short account gives a general explanation of 
the observed difference between results calculated for 
the discontinuous flow of a perfect fluid and those 
actually found by experiments in air and water, and 
if the nature of the flow over the back surface were 
accurately known, the value of « for the maximum 
of L/R could be predicted. Even in the absence of 
this knowledge, the assumption that surface friction 
varies as v* and acts only on the up-stream side, leads 
to a value of a that is not far removed from truth. 
Let AB, Fig. 4, be the plane making a small 
angle a@ with the stream, and let L and R be the 
lateral force and resistance which would be experi- 
enced if there were no friction. 
If L’ and R’ are the same quantities, taking fric- 
tion into account, and putting Fv’ as the frictional 
force parallel to AB, we have L’=L—Fa and 
R’=R+Fv?, and since L=R,a, and R=R,a’, R, 
being the normal resistance Av’, 
L’=L—Fa=av?(A,,—F), 
and 
R’=R+ Fv? =v7(Aa?+F); 
Be A 
Fic. 4. 
hence L’/R’=a(A—F)/(a?A+F), and this is a maxi- 
mum when a=/7F/R. 
Lanchester’s experiments make | F/R=o0-0075; 
Zahn’s experiments make F/R=o0-0037, which corre- 
spond to 2=6-5° or 3-5° respectively. 
The actual value found from direct experiments on 
L and R lies between these two, and although 6-5° 
is nearer the truth than 3-5°, this does not imply that 
00075 is the more nearly correct value of F/R, for 
the complete theory must take into consideration the 
action of the streams on both sides of the plane. 
If ascending currents can be found, or if use can 
be made of differences of speed in the wind at 
different levels, there is no reason why engineless 
flight should not succeed, but the opportunities are 
rather limited. 
The heaviest birds which can fly (great bustards, 
turkeys, and some of the vultures, eagles, and peli- 
cans) weigh between 20 and 30 lb. Of these, 
bustards and turkeys are short-winged, and the load 
is more than 2 Ib. to the square foot of wing. But 
their flights are short and their wing movements 
rapid, and the power expended while rising from the 
ground must be very great in proportion to their size. 
The large birds which make long flights have wing 
areas giving a load of less than 2 Ib. per square foot, 
and are all adepts at making use of ascending 
air currents, so that for the most part of their time in 
the air they have but little work to do. 
Much controversy has arisen on the question of the 
sufficiency of upward currents or upward components 
NO. 2219, VOL. 89] 
of currents of air to account for such flights, but the 
more the circumstances are examined the more clearly 
it appears that soaring is in most cases effected in 
this way, although the origins of the ascending 
currents are very various. Sometimes they are 
caused by natural obstructions in the path of the 
wind, such as cliffs, hills, the sides or sails of a ship, 
or the slope of waves, but on a larger scale they are 
chiefly the result of air ascending after having been 
warmed by contact, direct or indirect, with the 
ground. At low levels such vertical movements are 
very small, and at the surface of the ground any 
motion must, of course, be parallel to the surface; but 
at considerable heights, especially in sunny countries, 
these convection currents must always exist, even 
when the weather is calm, except in the rare event of 
large tracts of sea or country having the, same 
temperature as the air in contact with them. 
To anyone flying at a height, the sense of true 
vertical which we have, and by which we adjust our 
balance when standing or moving on the ground, is 
replaced by the direction of the resultant force of 
gravitation and any acceleration which the machine 
may be subject to. In still air or in a uniform wind, 
acceleration can only be the result of an alteration 
of level or of the engine speed, and the effects due 
to the latter cause cannot be very large or rapid. 
When, however, the machine passes quickly from a 
region of still air into a wind, or vice versd, which 
is what happens practically in gusts, the sensation of 
vertical direction is lost, and although the speed and 
direction of travel of the machine only change gradu- 
ally, the resultant of the forces acting on it does so 
instantaneously, not only in direction, but in magni- 
tude. 
The three diagrams in Fig. 5 show the direction 
in which a short pendulum at the centre of gravity 
of the machine would point (a) when the flight is in 
uniformly moving air, (b) when in an overtaking 
gust, (c) in an opposing gust. 
The connection between the angle (@) which the 
pendulum makes with the true vertical being 
Propulsive force — Resistance 
Lifting force ‘ 
It is hardly to be wondered at that such changes 
in the apparent vertical should be confusing to the 
pilot, and that accidents, which are often fatal, should 
happen while experience is being acquired. 
Side gusts may produce still more embarrassing 
effects, the character of which depends on the class of 
machine and the disposition of the wings to a greater 
degree than is the case with gusts in or against the 
direction of motion. 
At the present time the wings and framework of 
all machines are made as rigid as possible by wire 
stays, &c., with the result that the breakage of any 
one part is likely to wreck the whole, and it is 
probable that as time goes on more attention will be 
directed to increasing their pliability so as to allow a 
reasonable amount of distortion without crippling the 
structure. The problem of determining the greatest 
possible flexibility which can be given to a structure 
of a definite shape, size, and weight, which is also 
to have a definite initial stiffness, is theoretically 
capable of solution in terms of the strength, density, 
and dynamic worth of the materials (by dynamic 
worth is meant the worth which can be stored 
elastically in the unit volume), and although I am 
not aware that any case has been worked out, the 
subject is worthy of investigation. 
The most important questions which can be raised 
about flying machines relate to their stability in flight 
and the ease or difficulty of starting or stopping them, 
tan d= 
rs 7 er i'd 
