Art LXIV.—On the Sailing Flight of the Albatros; a Reply to Mr. J. S. Webb.*
[Read before the Auckland Institute, 13th June, 1870.]
In the second volume of the Transactions of the New Zealand Institute, p. 233, there appears a criticism by Mr. J. S. Webb, on a paper of mine, published in the “Phil. Mag.” for August, 1869, on the flight of the Albatros, in which he says that I have not been happy in the mathematical treatment of the subject, having made a mistake at the outset of my calculations, and that the higher velocities that he derives from my data upset the conclusions that I have drawn. I am, therefore, almost compelled, in self defence, to criticise a little his criticism.
Before commencing, however, I ought perhaps to inform those who have not read my paper, that the object I had in view in that part of it to which Mr. Webb has taken exception, was to show as clearly and as simply as possible, that if an albatros started with a certain velocity it could, by slightly altering the angle at which it was flying, continue to support itself in the air without using its wings until its velocity had been reduced below a certain point, and I, therefore, pointed out the two main principles on which this depended, and omitted many minor points which would have to be considered if fully discussing the case. Any person who reads my paper will see that these calculations make no pretensions to accuracy, for the data on which they are founded are merely rough approximations. They are simply used as an illustration, and rough demonstration, of a previously propounded theory (see “Ibis,” July, 1864); for, in order to prove the theory, both the resistance of the air to the bird and the velocities at which it sails must be obtained by observation and experiment, and they must then be shown by calculation to be not inconsistent with one another when connected according to the theory.
I will here, also, take the opportunity of explaining to those who notice discrepancies in my two papers, that after I had read the first to the Auckland Institute I received from England a copy of Dr. Pettigrew's paper on the flight of birds, and in the second paper (published in the “Phil. Mag.”) I used his observations on the angle which the wings of a bird make with its body, as giving probably a more accurate result than taking the wings and body to be in the same plane, as in my first paper; and not unnecessarily tocompli-
[Footnote] * See previous Articles, Vol. II., p. 227, and 233.
cate a subject in which no great accuracy was to be expected, I omitted the resistance of the air to the under surface of the body of the bird as being very small in comparison to that of the wings.
With these explanations I will now proceed to discuss the appendix to Mr. Webb's paper.
Page 234, line 4 from bottom, et seq.—“Captain Hutton first assumes that the number of feet the bird travels in one second = HE, and then that the bird will pass in the same time through the longer distance AE.”
Mr. Webb has here fallen into a mistake through not having comprehended my meaning, which may not, perhaps, have been very clearly expressed. HE represents the actual velocity of the bird, and is the only line that could be determined by observation. AE represents the distance it would have passed through but for the counteracting influence of gravity, and must be calculated from HE.
Page 234, line 2 from bottom, et seq.—“The mistake leads him (Capt. H.) to the further error of adopting HE tan AEH as the measure of the vertical component of the atmospheric resistance instead of HE sin AEH.”
Mr. Webb has again failed to comprehend my meaning, but this time from carelessness in reading my paper. AH is not taken by me to represent the height the bird would rise by atmospheric resistance, but by the direction in which the bird was flying—viz., slightly upwards; and this inattention has led him into the remark that I have “unaccountably adopted a totally different method to arrive at the vertical component of resistance in the case of the wings,” the truth being that I have adopted “totally different methods” for dealing with two totally different things—viz., the angle of flight in the first case, and the resistance of the air to the wings of the bird in the second. It will, therefore, be seen that it is not I, but Mr. Webb, who has arrived at the “strange conclusion” mentioned a few lines further on. Even if it had been the atmospheric resistance that was here being considered, HE sin AEH would not be the measure of the vertical component, for it is the measure of the whole of the resistance both to forward as well as to downward movement.
Page 235, line 16.—“The whole force exerted by the bird is, in fact, HE + R.” I do not know what Mr. Webb means by this, for HE does not represent a force at all, but the velocity of the bird, which is a very different thing, although it will, no doubt, have a certain ratio to the force exerted by the bird.
Page 235, lines 17–18.—“It is not LE but KE (= HE sin CEH) which represents the vertical component of the force actually at work.”
How KE can be supposed to represent the vertical component of any force is more than I can understand. It is the same error as that previously made with regard to HE sin AEH.
Page 235, line 21, et seq.—“Captain Hutton goes on to say ‘the total amount the bird will rise will be LE + HA feet.’ Introducing the corrections just made, this amounts to saying that the upward pressure on the whole area of the bird = HE (sin AEH + sin CEH). This is a grave error.”
No doubt it is, with Mr. Webb's additions and corrections, a very grave error indeed, but it is not of my making. The same confusion that has already been pointed out is again here very apparent. “The total amount the bird will rise,” is not by any means the same thing as “the upward pressure on the whole area of the bird,” although Mr. Webb has substituted one for the other. HE, HA, and LE, do not represent pressures, but spaces traversed in a certain time, or, in other words, velocities. As HE was originally taken to represent the velocity of the bird, or air (which must be the same thing), it could not possibly also represent the force or pressure of the air, which is a very different thing, although Mr. Webb has taken it to represent both. At the outset of my calculations I changed the pressure necessary to support the bird into an upward current of air moving with a velocity of 30 feet per second, and the problem then was to find what would be the horizontal velocity (HE) of the air which would give, when acted upon by the wings of the bird, a vertical component equal to 30. I then showed that when the bird was flying at an angle (AEH) with the horizon, the distance it would rise in a second (HE tan AEH) would have to be deducted from the 30. I next showed that when the velocity of the wind was HE, its vertical component, when acted on by the wings of the bird inclined at an angle CEH to the horizon, would be HE sin CEH cos CEH, and that, therefore, the two must together be made equal to 30 to enable us to find what the horizontal velocity of the wind (HE) should be, in order that it might just counteract the force of gravity. I must, however, here confess that, owing to a lapsus calami, I have, unfortunately, written in my paper “the force of the wind HE,” instead of “the velocity of the wind HE,” and twice afterwards, where the word “force” has been employed, it would perhaps have been better to have used the word “direction, “and although this slip has in no way affected my subsequent reasoning, it may have confused Mr. Webb and led to his mistakes. So far, therefore, I must plead guilty, but I cannot allow that he has upset any conclusion that I have drawn; on the contrary, he has supplied me with a formula, which, as I shall presently show, completely gets over the only difficulty in the way of my theory.
Mr. Webb's equation (1) is not correct, for, as I have shown, HE sin AEH and HE sin CEH are not the vertical components of the resistance of the air, and equation (2) is not a legitimate deduction from (1), as in it force and velocity are confused together, consequently (3) and (4) are incorrect also.
I agree with Mr. Webb that it is hardly fair to compare an Albatros with
a round shot, not, however, because a round shot is a projectile, for an Albatros when sailing is a true projectile also, but because the initial velocities are so very different. Instead, therefore, of the round shot formula I will take the one given by Mr. Webb.
R=½ Q v2 sin3 I. A.
and take the body of the Albatros to be a cone of 20°. We shall then have
R=0.0006 sin3 10 A v2
R=0.000003 A v2
which is very nearly that which I calculated would allow an Albatros to sail for half an hour, and is just half way between the resistances calculated in my first and second papers; and, therefore, if this formula may be relied upon, all the difficulties of my theory disappear, for, although something would have to be added for the resistance to the wings, something would also have to be deducted for the tapering away of the hinder parts of the bird, which is known to decrease the resistance considerably. At page 234, line 6, Mr. Webb remarks, “I do not know whether the merit of the demonstration belongs to him (Captain Hutton), he appears to claim it.” I may, therefore, I hope, without being considered egotistical, be allowed to make a few remarks on the subject. In 1864, when I first took up the question, the prevailing opinions about it were various and confused, as pointed out by me in the previous paper that I read to the Auckland Institute. Even those authors who had seen that sailing flight must be due to previous momentum (such as Darwin in his account of the flight of the Condor), had no clear ideas of how the two were connected, and thought that probably the momentum was kept up, or increased, by the bird occasionally closing its wings and falling rapidly for some distance. I was, I believe, the first, in March, 1865, to enunciate the theory that it was by slightly increasing the angle of flight that a bird was enabled to sail, and my paper published in the “Phil. Mag.” for August, 1869, was, I believe, the first attempt made to treat the subject mathematically, and to show, not only the mechanical principles on which it depended, but also that the resistance of the air was no insuperable objection to my theory. This is all I claim, and I do not know that any one has ever disputed either the truth of the theory, or my priority in enunciating it. A German named Prechtl, and a Frenchman named, I think, Maret, have both written books on the flight of birds, but they are rare and but little known, and I have not seen either of them, nor do I know the dates of their publication, and it is possible that I may have been forestalled by one or other of them.