THE SHAPE AND EFFICIENCY OF AEROPLANES.
In Prof. Langley’s lifetime, we had many discussions regarding the width
and shape of aeroplanes. The Professor had made many experiments with
very small and narrow planes, and was extremely anxious to obtain some
data regarding the effect that would be produced by making the planes of
greater width. He admitted that by putting some two or three aeroplanes
tandem, and all at the same angle, the front aeroplane _a_ (Fig. 57),
would lift a great deal more than _b_, and that _c_, would lift still
less. He suggested the arrangement shown at _a′_, _b′_, _c′_, in which
_b′_ is set at such an angle as to give as much additional acceleration
to the air as it had received in the first instance by passing under
_a′_, and that _c′_, should also increase the acceleration to the same
extent. With this arrangement, the lifting effect of the three
aeroplanes ought to be the same, but I did not agree with this theory.
It seemed to me that it would only be true if it dealt with the volume
of air represented between _j_, and _k_, and that he did not take into
consideration the mass of air between _k_, and _l_, that had to be dealt
with, and which would certainly have some effect in buoying up the
stream of air, _j_, _k_. Prof. Langley admitted the truth of this, and
said that nothing but experiment would demonstrate what the real facts
were. But it was a matter which I had to deal with. I did not like the
arrangement _a′_, _b′_, _c′_, as the angle was so sharp, especially at
_c′_, that a very large screw thrust would be necessary. I therefore
made a compromise on this system which is shown at _a′′_, _b′′_, _c′′_.
In this case _a′′_, has an inclination of 1 in 10, _b′′_ an inclination
of 1 in 6, and _c′′_ an inclination of 1 in 5. It will be seen that this
form, which is shown as one aeroplane at _a′′′_, _b′′′_, _c′′′_, is a
very good shape. It is laid out by first drawing the line _c_, _d_,
dropping the perpendicular equal to one-tenth of the distance between
_c_ and _d_, and then drawing a straight line from _c_, through _e_, to
_f_, where another perpendicular is dropped, and half the distance
between _d_ and _e_ laid off, and another straight line drawn from _e_,
through _g_, to _h_, and the perpendicular _h_, _i_, laid off the same
as _f_, _g_. We then have four points, and by drawing a curve through
these, we obtain the shape of the aeroplane shown above, which is an
exceedingly good one. This shape, however, is only suitable for
velocities, up to 40 miles per hour; at higher velocities, the curvature
would be correspondingly reduced.
[Illustration: Fig. 57.--Diagram showing the evolution of a wide
aeroplane.]
THE ACTION OF AEROPLANES AND THE POWER REQUIRED EXPRESSED IN THE
SIMPLEST TERMS.
In designing aeroplanes for flying machines, we should not lose sight of
the fact that area alone is not sufficient. Our planes must have a
certain length of entering edge--that is, the length of the front edge
must bear a certain relation to the load lifted. An aeroplane 10 feet
square will not lift half as much for the energy consumed as one 2 feet
wide and 50 feet long; therefore, we must have our planes as long as
possible from port to starboard. At all speeds of 40 miles per hour or
less, there should be at least 1 foot of entering edge for every 4 lbs.
carried. However, at higher speeds, the length may be reduced as the
square of the speed increases. An aeroplane 1 foot square will not lift
one-tenth as much as one that is 1 foot wide and 10 feet long. This is
because the air slips off at the ends, but this can be prevented by a
thin flange, or _à la_ Hargrave’s kites. An aeroplane 2 feet wide and
100 feet long placed at an angle of 1 in 10, and driven edgewise through
the air at a velocity of 40 miles per hour, will lift 2·5 lbs. per
square foot. But as we find a plane 100 feet in length too long to deal
with, we may cut it into two or more pieces and place them one above the
other--superposed. This enables us to reduce the width of our machine
without reducing its lifting effect; we still have 100 feet of entering
edge, we still have 200 feet of lifting surface, and we know that each
foot will lift 2·5 lbs. at the speed we propose to travel. 200 × 2·5 =
500; therefore our total lifting effect is 500 lbs., and the screw
thrust required to push our aeroplane through the air is one-tenth of
this, because the angle above the horizontal is 1 in 10. We, therefore,
divide what Prof. Langley has so aptly called the “lift” by 10; 500/10
= 50. It will be understood that the vertical component is the lift, and
the horizontal component the drift, the expression “drift” also being a
term first applied by Prof. Langley. Our proposed speed is 40 miles per
hour, or 3,520 feet in a minute of time. If we multiply the drift in
pounds by the number of feet travelled in a minute of time, and divide
the product thus obtained by 33,000, we ascertain the H.P. required--
50 × 3,520
---------- = 5·33.
33,000
It therefore takes 5·33 H.P. to carry a load of 500 lbs. at a rate of 40
miles per hour, allowing nothing for screw slip or atmospheric
resistance due to framework and wires. But we find we must lift more
than 500 lbs., and as we do not wish to make our aeroplanes any longer,
we add to their width in a fore and aft direction--that is, we place
another similar aeroplane, also 2 feet wide, just aft of our first
aeroplane. This will, of course, have to engage the air discharged from
the first, and which is already moving downwards. It is, therefore, only
too evident that if we place it at the same angle as our first
one--viz., 1 in 10--it will not lift as much as the first aeroplane, and
we find that if we wish to obtain a fairly good lifting effect, it must
be placed at an angle of 1 in 6. Under these conditions, the screw
thrust for this plane will be 1/6th part of the lift, or 8·88 H.P.
against 5·33 H.P. with our first aeroplane. In order to avoid confusion,
we will call our first plane _a′′_, our second plane _b′′_, and the
third _c′′_, the same as in Fig. 57. Still we are not satisfied, we want
more lift, we therefore add still another aeroplane as shown (_c′′_,
Fig. 57). This one has to take the air which has already been set in
motion by the two preceding planes _a′′_ and _b′′_, so in order to get a
fair lifting effect, we have to place our third plane at the high angle
of 1 in 5. At this angle, our thrust has to be 1/5th of the lifting
effect, and the H.P. required is twice as much per pound carried as with
the plane _a′′_, where the angle was 1 in 10; therefore, it will take
10·66 H.P. to carry 500 lbs. As there is no reason why we should have
three aeroplanes placed tandem where one would answer the purpose much
better, we convert the whole of them into one, as shown (_a′′′_, _b′′′_,
_c′′′_, Fig. 57), and by making the top side smooth and uniform, we get
the advantage of the lifting effect due to the air above the aeroplane
as well as below it. The average H.P. is therefore 5·33 + 8·88 + 10·66 ÷
3 = 8·29 H.P. for each plane, or 25 H.P. for the whole, which is at the
rate of 60 lbs. to the H.P., all of which is used to overcome the
resistance due to the weight and the inclination of the aeroplanes, and
which is about half the total power required. We should allow as much
more for loss in screw slip and atmospheric resistance due to the motor,
the framework, and the wires of the machine. If, however, the screw is
placed in the path of the greatest resistance, it will recover a portion
of the energy imparted to the air. We shall, however, require a 50 H.P.
motor, and thus have 30 lbs. to the H.P.
From the foregoing it will be seen that at a speed of 40 miles an hour,
the weight per H.P. is not very great. If we wish to make a machine more
efficient, we must resort to a multitude of very narrow superposed
planes, or sustainers, as Mr. Philipps calls them, or we must increase
the speed. If an aeroplane will lift 2·5 lbs. per square foot placed at
an angle of 1 in 10, and driven at a velocity of 40 miles an hour, the
same aeroplane will lift 1·25 lbs. if placed at an angle of 1 in 20, and
as the lifting effect varies as the square of the velocity, the same
plane will lift as much more at 60 miles per hour, as 60² is greater
than 40²--that is, 2·81 lbs. per square foot instead of 1·25 lbs. At
this high speed, providing that the width of the plane is not more than
3 feet, it need be only slightly curved and have a mean angle of 1 in
20.
An aeroplane 100 feet long and 3 feet wide would have 300 square feet of
lifting surface, each of which would lift 2·81 lbs., making the total
lifting effect 843 lbs. 843 ÷ 20 = 42·15, which is the screw thrust that
would be necessary to propel such a plane through the air at a velocity
of 60 miles per hour. 60 miles per hour is 5,280 feet in a minute,
therefore the H.P. required is 42·15 × 5,280 ÷ 33,000 = 6·7 H.P.
Dividing the total lifting effect 843 by 6·7, we have 843 ÷ 6·7 = 125·8,
the lift per H.P. If we allow one-half for loss in friction, screw slip,
etc., we shall be carrying a load of 843 lbs. with 13·4 H.P. It will,
therefore, be seen that a velocity of 60 miles an hour is much more
economical in power than the comparatively low velocity of 40 miles an
hour; moreover, it permits of a considerable reduction in the size and
weight of the machine, and this diminishes the atmospheric resistance.
[Illustration: Fig. 58.--In a recently published mathematical treatise
on Aerodynamics, an illustration is shown, representing the path that
the air takes on encountering a rapidly moving curved aeroplane. It will
be observed that the air appears to be attracted upwards before the
aeroplane reaches it, exactly as iron filings would be attracted by a
magnet, and that the air over the top of the aeroplane is thrown off at
a tangent, producing a strong eddying effect at the top and rear. Just
why the air rises up before the aeroplane reaches it is not plain, and
as nothing could be further from the facts, mathematical formulas
founded on such a mistaken hypothesis can be of but little value to the
serious experimenter on flying machines.]
[Illustration: Fig. 59.--An illustration from another scientific
publication also on the Dynamics of Flight. It will be observed that the
air in striking the underneath side of the aeroplane is divided into two
streams, a portion of it flowing backwards and over the top of the edge
of the aeroplane where it becomes compressed. An eddy is formed on the
back and top of the aeroplane, and the air immediately aft the aeroplane
is neither rising nor falling. Just how these mathematicians reason out
that the air in striking the front of the aeroplane would jump backwards
and climb up over the top and leading edge against the wind pressure is
not clear.]
[Illustration: Fig. 60.--This shows another illustration from the same
mathematical work, and represents the direction which the air is
supposed to take on striking a flat aeroplane. With this, the air is
also divided, a portion moving forward and over the top of the aeroplane
where it is compressed, leaving a large eddy in the rear, and, as the
dotted lines at the back of the aeroplane are horizontal, it appears
that the air is not forced downwards by its passage. Here, again,
formula founded on such hypothesis is misleading in the extreme.]
[Illustration: Fig. 61.--This shows the shape and the practical angle of
an aeroplane. This angle is 1 in 10, and it will be observed that the
air follows both the upper and the lower surface, and that it leaves the
plane in a direction which is the resultant of the top and bottom
angle.]
[Illustration: Fig. 62.--This shows an aeroplane of great thickness,
placed at the highest angle that will ever be used--1 in 4--and even
with this the air follows the upper and lower surfaces. No eddies are
formed, and the direction that the air takes after leaving the aeroplane
is the resultant of the top and bottom angles.]
[Illustration: Fig. 63.--Section of a screw blade having a rib on the
back. The resistance caused by this rib is erroneously supposed to be
skin friction.]
[Illustration: Fig. 64.--Shows a flat aeroplane placed at an angle of
45°, an angle which will never be used in practical flight, but at this
angle the momentum of the approaching air and the energy necessary to
give it an acceleration sufficiently great to make it follow the back of
the aeroplane are equal, and at this point, the wind may either follow
the surface or not. Sometimes it does and sometimes it does not. See
experiments with screws.]
[Illustration: Fig. 65.--The aeroplane here shown is a mathematical
paradox. This aeroplane lifts, no matter in which direction it is
driven. It encounters air which is stationary and leaves it with a
downward trend; therefore it must lift. However, if we remove the
section _b_, and only subject _a_ to the blast, as shown at Fig. 66, no
lifting effect is produced. On the contrary, the air has a tendency to
press _a_, downwards. The path which the air takes is clearly shown;
this is most important, as it shows that the shape of the top side is a
factor which has to be considered. All the lifting effect in this case
is produced by the top side.]
[Illustration: Fig. 66.]
[Illustration: Fig. 67.--In this drawing _a_ represents an aeroplane, or
a bird’s wing. Suppose that the wind is blowing in the direction of the
arrows; the real path of the bird as relates to the air is from _i_ to
_j_,--that is, the bird is falling as relates to the air although moving
on the line _c_, _d_, against the wind. In some cases, a bird is able to
travel along the line _g_, _h_, instead of in a horizontal direction,
thus rising and apparently flying into the teeth of the wind at the same
time.]
SOME RECENT MACHINES.
Professor S. P. Langley, of the Smithsonian Institute, Washington, D.C.,
made a small flying model in 1896. This, however, only weighed a few
pounds; but as it did actually fly and balance itself in the air, the
experiment was of great importance, as it demonstrated that it was
possible to make a machine with aeroplanes so adjusted as to steer
itself automatically in a horizontal direction. In order to arrive at
this result, an innumerable number of trials were made, and it was only
after months of careful and patient work that the Professor and his
assistants succeeded in making the model fly in a horizontal direction
without rearing up in front, and then pitching backwards, or plunging
while moving forward.
The Wright Brothers of Dayton, Ohio, U.S.A., often referred to as “the
mysterious Wrights,” commenced experimental work many years ago. The
first few years were devoted to making gliding machines, and it appears
that they attained about the same degree of success as many others who
were experimenting on the same lines at the same time; but they were not
satisfied with mere gliding machines, and so turned their attention in
the direction of motors. After some years of experimental work, they
applied their motor to one of their large gliding machines, and it is
said that with this first machine they actually succeeded in flying
short distances. Later on, however, with a more perfect machine, they
claim to have made many flights, amongst which I will mention three: 12
miles in 20 minutes, on September 29th, 1905; 20·75 miles in 33 minutes,
on October 4th; and 24·2 miles in 38 minutes, on October 5th of the same
year. As there seems to be much doubt regarding these alleged flights,
we cannot refer to them as facts until the Wright Brothers condescend to
show their machine and make a flight in the presence of others;
nevertheless, I think we are justified in assuming that they have met
with a certain degree of success which may or may not be equal to the
achievements of Messrs Farman and De la Grange. It is interesting to
note in this connection that all flying machines that have met with any
success have been made on the same lines; all have superposed
aeroplanes, all have fore and aft horizontal rudders, and all are
propelled with screws; and in this respect they do not differ from the
large machine that I made at Baldwyn’s Park many years ago. I have seen
both the Farman and the De la Grange machines; they seem to be about the
same in size and design, and what is true of one is equally true of the
other; I will, therefore, only describe the one that seems to have done
the best--the De la Grange. The general design of this machine is
clearly shown in the illustrations (Figs. 68 and 69). The dimensions are
as follows: The two main aeroplanes are 32·8 feet long and 4·9 feet
wide; the tail or after rudder is made in the form of a Hargrave’s box
kite, the top and bottom sides of the box being curved and covered with
balloon fabric, thus forming aeroplanes. This box is 9·84 feet long from
port to starboard, and 6·56 feet wide in a fore and aft direction. The
diameter of the screw is 7·2 feet and it has a mean pitch of 5·7 feet.
The screw blades are two in number and are extremely small, being only
6·3 inches wide at the outer end and 3·15 inches at the inner end, their
length being 2·1 feet. The space between the fore and aft aeroplanes is
4·9 feet. The total weight is about 1,000 lbs. with one man on board.
The speed of this machine through the air is not known with any degree
of certainty; it is, however, estimated to be 32 to 40 miles per hour.
When the screw is making 1,100 revolutions per minute, the motor is said
to develop 50 H.P.
[Illustration: Fig. 68.--The De la Grange machine on the ground and
about to make a flight.]
[Illustration: Fig. 69.--The De la Grange machine in full flight and
very near the ground.]
In the following calculations, I have assumed that the machine has the
higher speed--40 miles per hour. I have been quite unable to obtain any
reliable data regarding the angle at which the aeroplanes are set, but
it would appear that the angle is about 1 in 10. The total area of the
two main aeroplanes is 321·4 square feet. A certain portion of the lower
main aeroplane is cut away, but this is compensated for by the forward
horizontal rudder placed in the gap thus formed. The two rear aeroplanes
forming the tail of the machine have an area of 128·57 square feet. The
area of all the aeroplanes is, therefore, 450 square feet. As the weight
of the machine is 1,000 lbs., the lift per square foot is 2·2 lbs.
Assuming that the angle of the aeroplanes is 1 in 10, the screw thrust
would be 100 lbs., providing, however, that the aeroplanes were perfect
and no friction of any kind was encountered. Forty miles per hour is at
the rate of 3,520 feet in a minute of time, therefore, (3,520 ×
100)/33,000 = 10·66 H.P. If we allow another 10 H.P. for atmospheric
resistance due to the motor, the man, and the framework of the machine,
it would require 20·66 H.P. to propel the machine through the air at the
rate of 40 miles per hour. If the motor actually develops 50 H.P., 29
H.P. will be consumed in screw slip and overcoming the resistance due
to the imperfect shape of the screw. The blades of the De la Grange
screw propeller are extremely small, and the waste of energy is,
therefore, correspondingly great--their projected area being only 1·6
square feet for both blades. Allowing 200 lbs. for screw thrust, we have
the following: 200/1·60 = 125 lbs. pressure per square foot on the
blades. If we multiply the pitch of the screw in feet by the number of
revolutions per minute, we find that if it were travelling in a solid
nut it would advance over 70 miles an hour. By the Eiffel tower formula
P = 0·003 V², a wind blowing at a velocity of 70 miles per hour produces
a pressure of 14·7 lbs. per square foot on a normal plane; therefore,
assuming that the projected area of the screw blades is 1·6, we have 1·6
× 14·7 = 23·52 lbs., which is only one-fifth part of what the pressure
really is when the screws are making 1,100 turns a minute. It is
interesting to note that the ends of the screw blades travel at a
velocity of 414 feet per second, which is about one-half the velocity of
a cannon ball fired from an old-fashioned smooth bore.
[Illustration: Fig. 70.--Farman’s machine in flight].
A flying machine has, of course, to be steered in two directions at the
same time--the vertical and the horizontal. In the Farman and De la
Grange machines, the horizontal steering is effected by a small windlass
provided with a hand wheel, the same as on a steam launch, and the
vertical steering is effected by a longitudinal motion of the shaft of
the same windlass. As the length of the machine is not very great, it
requires very close attention on the part of the man at the helm to keep
it on an even keel; if one is not able to think and act quickly,
disaster is certain. On one occasion, the man at the wheel pushed the
shaft of the windlass forward when he should have pulled it back, and
the result was a plunge and serious damage to the machine; happily no
one was injured, though some of the bystanders were said to have had
very narrow escapes. The remedy for this is to make all hand-steered
machines of great length, which gives more time to think and act; or,
still better, to make them automatic by the use of a gyroscope.
[Illustration: Fig. 71.--Bleriot’s machine. This machine raised itself
from the ground, but as the centre of gravity was very little, if any,
above the centre of lifting effect, it turned completely over in the
air.]
[Illustration: Fig. 72.--Santos Dumont’s flying machine.]
VELOCITY AND PRESSURE OF THE WIND.
The pressure varies as the square of the velocity or P ∝ V². The old
formula for wind blowing against a normal plane was P = 0·005 × V².
The latest or Eiffel Tower formula gives a much smaller value, being P
= 0·003 × V², where V represents the velocity in miles per hour, and P
the pressure in pounds per square foot.
+---------------------------------+---------+----------------------+
| VELOCITY. |Pressure | |
| | on a |Character of the Wind.|
+---------+-----------+-----------+Sq. Foot.| |
|Per Hour.|Per Minute.|Per Second.| | |
+---------+-----------+-----------+---------+----------------------+
| Miles. | Feet. | Feet. | Lbs. | |
| 1 | 88 | 1·5 | ·003 | Barely observable. |
| 2 | 176 | 2·9 | ·012 |} Just |
| 3 | 264 | 4·4 | ·027 |} perceptible. |
| 4 | 352 | 5·9 | ·048 | Light breeze. |
| 5 | 440 | 7·3 | ·075 |} Gentle, |
| 6 | 528 | 8·8 | ·108 |} pleasant |
| 8 | 704 | 11·7 | ·192 |} wind. |
| 10 | 880 | 14·7 | ·3 | Fresh breeze. |
| 15 | 1,320 | 22 | ·675 | Brisk breeze. |
| 20 | 1,760 | 29·4 | 1·2 | Stiff breeze. |
| 25 | 2,200 | 36·7 | 1·875 | Very brisk breeze. |
| 30 | 2,640 | 44 | 2·7 |} High |
| 35 | 3,080 | 51·3 | 3·675 |} wind. |
| 40 | 3,520 | 58·7 | 4·8 | Very high wind. |
| 45 | 3,960 | 66 | 6·075 | Gale. |
| 50 | 4,400 | 73·4 | 7·5 | Storm. |
| 60 | 5,280 | 88 | 10·8 |} Great |
| 70 | 6,160 | 102·7 | 14·7 |} storm. |
| 80 | 7,040 | 117·2 | 19·2 | Hurricane. |
| 90 | 7,920 | 132 | 24·3 |} |
| 100 | 8,800 | 146·7 | 30 |} Tornado. |
| 110 | 9,680 | 161·2 | 36·3 | } |
| 120 | 10,560 | 176 | 43·2 | } “Washoe |
| 130 | 11,440 | 191 | 50·7 | } zephyrs.”[2] |
| 140 | 12,320 | 205·3 | 58·8 | } |
| 150 | 13,200 | 220 | 67·5 | } |
+---------+-----------+-----------+---------+----------------------+
[2] With apologies to Mark Twain.
[Illustration: Fig. 72_a_.--Angles and degrees compared. It will be
observed that an angle of 1 in 4 is practically 14°.]
TABLE OF EQUIVALENT INCLINATIONS.
+------------+----------------+-------------------+
| Rise. | Sine of Angle. | Angle in Degrees. |
+------------+----------------+-------------------+
| 1 in 30, | ·0333 | 1·91 |
| 1 „ 25, | ·04 | 2·29 |
| 1 „ 20, | ·05 | 2·87 |
| 1 „ 18, | ·0555 | 3·18 |
| 1 „ 16, | ·0625 | 3·58 |
| 1 „ 14, | ·0714 | 4·09 |
| 1 „ 12, | ·0833 | 4·78 |
| 1 „ 10, | ·1 | 5·73 |
| 1 „ 9, | ·1111 | 6·38 |
| 1 „ 8, | ·125 | 7·18 |
| 1 „ 7, | ·143 | 8·22 |
| 1 „ 6, | ·1667 | 9·6 |
| 1 „ 5, | ·2 | 11·53 |
| 1 „ 4, | ·25 | 14·48 |
| 1 „ 3, | ·3333 | 19·45 |
+------------+----------------+-------------------+
TABLE OF EQUIVALENT VELOCITIES.
+-----------+-------------+-------------+-------------+-------------+
| | | | | |
| Miles | Feet | Feet | Metres | Metres |
| per Hour. | per Second. | per Minute. | per Minute. | per Second. |
+-----------+-------------+-------------+-------------+-------------+
| | | | | |
| 1, | 1·5 | 88 | 26·8 | ·447 |
| 2, | 2·9 | 176 | 53·6 | ·894 |
| 3, | 4·4 | 264 | 80·5 | 1·341 |
| 4, | 5·9 | 352 | 107·3 | 1·788 |
| 5, | 7·3 | 440 | 134·1 | 2·235 |
| 6, | 8·8 | 528 | 160·9 | 2·682 |
| 8, | 11·7 | 704 | 214·6 | 3·576 |
| 10, | 14·7 | 880 | 268·2 | 4·470 |
| 15, | 22 | 1,320 | 402·3 | 6·705 |
| 20, | 29·4 | 1,760 | 536·4 | 8·940 |
| 25, | 36·7 | 2,200 | 670·5 | 11·176 |
| 30, | 44 | 2,640 | 804·6 | 13·411 |
| 35, | 51·3 | 3,080 | 938·8 | 15·646 |
| 40, | 58·7 | 3,520 | 1,072·9 | 17·881 |
| 45, | 66 | 3,960 | 1,207 | 20·116 |
| 50, | 73·4 | 4,400 | 1,341·1 | 22·352 |
| 60, | 88 | 5,280 | 1,609·2 | 26·822 |
| 70, | 102·7 | 6,160 | 1,877·5 | 31·292 |
| 80, | 117·2 | 7,040 | 2,145·8 | 35·763 |
| 90, | 132 | 7,920 | 2,414 | 40·233 |
| 100, | 146·7 | 8,800 | 2,682·2 | 44·704 |
| 110, | 161·2 | 9,680 | 2,950·2 | 49·174 |
| 120, | 176 | 10,560 | 3,218·4 | 53·644 |
| 130, | 191 | 11,440 | 3,486·6 | 58·115 |
| 140, | 205·3 | 12,320 | 3,755·1 | 62·585 |
| 150, | 220 | 13,200 | 4,023·3 | 67·056 |
+-----------+-------------+-------------+-------------+-------------+
To convert feet per minute into metres per second, multiply by ·00508.
TABLE SHOWING VELOCITY AND THRUST CORRESPONDING WITH VARIOUS
HORSE-POWERS.
+---------+-------------------------------------------------+
|Velocity | Horse-Power. |
|in Miles +------+-------+-------+--------+--------+--------+
|per Hour.| 1 | 10 | 20 | 30 | 40 | 50 |
| +------+-------+-------+--------+--------+--------+
| | Thrust in Pounds. |
+---------+------+-------+-------+--------+--------+--------+
| 1, |375 |3,750 |7,500 |11,250 |15,000 |18,750 |
| 5, | 75 | 750 |1,500 | 2,250 | 3,000 | 3,750 |
| 10, | 37·5 | 375 | 750 | 1,125 | 1,500 | 1,875 |
| 15, | 25 | 250 | 500 | 750 | 1,000 | 1,250 |
| 20, | 18·8 | 187·5| 375 | 562·5| 750 | 937·5|
| 25, | 15 | 150 | 300 | 450 | 600 | 750 |
| 30, | 12·5 | 125 | 250 | 375 | 500 | 625 |
| 35, | 10·7 | 107·1| 214·3| 321·4| 428·6| 535·7|
| 40, | 9·4 | 93·8| 187·5| 281·3| 375 | 468·8|
| 45, | 8·3 | 83·3| 166·7| 250 | 333·3| 416·7|
| 50, | 7·5 | 75 | 150 | 225 | 300 | 375 |
| 60, | 6·3 | 62·5| 125 | 187·5| 250 | 312·5|
| 70, | 5·4 | 53·6| 107·1| 160·7| 214·3| 267·9|
| 80, | 4·7 | 46·9| 93·8| 140·6| 187·5| 234·4|
| 90, | 4·2 | 41·7| 83·3| 125 | 166·7| 208·3|
| 100, | 3·75| 37·5| 75 | 112·5| 150 | 187·5|
+---------+------+-------+-------+--------+--------+--------+
+---------+--------------------------------------------+
|Velocity | Horse-Power. |
|in Miles +--------+--------+--------+--------+--------+
|per Hour.| 60 | 70 | 80 | 90 | 100 |
| +--------+--------+--------+--------+--------+
| | Thrust in Pounds. |
+---------+--------+--------+--------+--------+--------+
| 1, |22,500 |26,250 |30,000 |33,750 |37,500 |
| 5, | 4,500 | 5,250 | 6,000 | 6,750 | 7,500 |
| 10, | 2,250 | 2,625 | 3,000 | 3,375 | 3,750 |
| 15, | 1,500 | 1,750 | 2,000 | 2,250 | 2,500 |
| 20, | 1,125 | 1,312·5| 1,500 | 1,687·5| 1,875 |
| 25, | 900 | 1,050 | 1,200 | 1,350 | 1,500 |
| 30, | 750 | 875 | 1,000 | 1,125 | 1,250 |
| 35, | 642·8| 750 | 857·1| 964·3| 1,071·4|
| 40, | 562·5| 656·3| 750 | 843·8| 937·5|
| 45, | 500 | 583·3| 666·7| 750 | 833·3|
| 50, | 450 | 525 | 600 | 675 | 750 |
| 60, | 375 | 437·5| 500 | 562·5| 625 |
| 70, | 321·4| 375 | 428·6| 482·1| 535·7|
| 80, | 281·3| 328·2| 375 | 421·9| 468·8|
| 90, | 250 | 291·7| 333·3| 375 | 416·7|
| 100, | 225 | 262·5| 300 | 337·5| 375 |
+---------+--------+--------+--------+--------+--------+
[Illustration: Fig. 72_b_.--When an aeroplane is driven through the air,
it encounters stationary air and leaves it with a downward trend. With a
thick curved aeroplane, as shown, the air follows both the top and the
bottom surfaces, and the direction that the air takes is the resultant
of these two streams of air. It will be seen that the air takes the same
direction that it would take if the plane were flat, and raised from _a_
to _c_, which would be substantially the same as shown at _f_, _h_, _g_.
It has, however, been found by actual experiment that the curved plane
is preferable, because the lifting effect is more evenly distributed,
and the drift is less in proportion to the lift.]
[Illustration: Fig. 72_c_.--Aeroplanes experimented with by Mr. Horatio
Philipps. In the published account which is before me, the angles at
which these planes were placed are not given, but, by comparing the lift
with the drift, we may assume that it was about 1 in 10.
Fig. 5 seems to have been the best shape, and I find that this plane
would have given a lifting effect of 2·2 lbs. per square foot at a
velocity of 40 miles per hour.]
PHILIPPS’ EXPERIMENTS.
+----------+----------+------------+------------+------------+------+
| DESCRIP- | SPEED OF | DIMENSIONS | LIFT. | DRIFT. | |
| TION | AIR | OF | | | LIFT |
| OF | CURRENT. | AEROPLANES.| | | DI- |
| FORM. +----+-----+ +------+-----+------+-----+ VIDED|
| |Feet|Miles| |Whole | Lbs.|Whole | Lbs.| BY |
| |per | per | |Plane.| per |Plane.| per |DRIFT.|
| |sec.|hour.| | Ozs. | sq. | Ozs. | sq. | |
| | | | | | ft. | | ft. | |
+----------+----+-----+------------+------+-----+------+-----+------+
|Plane sur-| | | | | | | | |
|faces, | 39 |26·59| 16" × 5" | 9 |1·013| 2 |0·225| 4·5 |
|Fig. 1, | 60 |40·91| 16" × 1·25"| 9 |4·05 | 0·87 |0·392| 10·3 |
| „ 2, | 48 |32·73| 16" × 3" | 9 |1·688| 0·87 |0·163| 10·3 |
| „ 3, | 44 |30 | 16" × 3" | 9 |1·688| 0·87 |0·163| 10·3 |
| „ 4, | 44 |30 | 16" × 5" | 9 |1·013| 0·87 |0·098| 10·3 |
| „ 5, | 39 |26·59| 16" × 5" | 9 |1·013| 0·87 |0·098| 10·3 |
| „ 6, | 27 |18·41| 16" × 5" | 9 |1·013| 2·25 |0·253| 4 |
| | | |Area sq. ft.| | | | | |
|Rook’s | | | | | | | | |
|wing, | 39 |26·59| 0·5 | 8 |1·0 | 1·0 |0·125| 8 |
+----------+----+-----+------------+------+-----+------+-----+------+