Structural Limitations on the Power Output of the Pigeon’s Flight Muscles

The arrangement of muscles by which the wing of a bird is raised and lowered in flapping flight is well known to all who have done a class dissection of the pigeon (Saunders & Manton, 1959). It is generally accepted from inspection of the anatomy that the work in flapping flight is done by two muscles, the pectoralis, which depresses the humerus, and the supracoracoideus, which elevates it. It is of interest in the theory of bird flight to estimate the power transmitted to the wing by these muscles. Past estimates have been made by multiplying the weight of the two flight muscles by some figure for the power output per unit weight of these muscles, but as the latter figure can only be guessed within rather wide limits, these estimates are not very reliable.

In the present paper an attempt is made to estimate an upper limit to the power which could be transmitted to the humerus, by measuring the breaking tension of the insertion of each muscle, its amplitude of movement, and the maximum frequency of wingbeat (observed at take-off). A lower limit is obtained from observed climbing performance of tame pigeons.

If a muscle shortens through a distance I cm., exerting a force F dynes, then the work done is IF ergs. If the muscle contracts repetitively, n times per second, then the power output (or rate of doing work) is nlF ergs/sec. or nlF × 10⁻⁷ Watts.

The distance I through which the muscle insertion moves in a maximal contraction is easily measured, and the maximum number of times the movement can be repeated per second can be observed in the intact animal. The force F cannot be directly observed, and no doubt varies as the contraction proceeds. However, it obviously cannot exceed the force at which the muscle insertion breaks. If F is taken to be equal to this breaking force a figure for power output is obtained which is the maximum that the system could conceivably transmit—i.e. if P_max is the maximum possible power which could be transmitted, and F_b the force needed to break the insertion, then P_max. = nlF_b.

In practice the power output will of course be less than this. Since I and n are directly measured, this statement is equivalent to saying that the force exerted in actual contractions is less than the breaking force.

If, for instance, it were found that the power output from the wing muscles never actually exceeded P_max, this would imply that the force in the muscle never exceeded half that needed to break the insertion. The insertion would then be said to have a safety factor of 2 on tensile strength, meaning that it was twice as strong as needed to bear the maximum force met with in practice.

As implied by the term ‘safety factor’, extra strength gives safety in bearing abnormally high transient loads, during ineptly executed manœuvres for example. On the other hand, extra strength involves extra weight, requiring more power to fly. The bird is therefore under selection pressure to make its structural parts just strong enough to meet any loads likely to be met with in practice, and no stronger.

To get an approximation for the safety factor on tensile strength of the insertions of the flight muscles, a figure is needed for the minimum power which would account for observed flight performance.

The power exerted by a bird in steady horizontal flight is not readily accessible to measurement or estimate. However, pigeons startled from feeding on the ground can be induced to climb very steeply for a few feet before accelerating away in horizontal flight, and if the initial steep climbing phase is timed, a figure can be obtained for the pigeon’s vertical speed.

A pigeon of weight W dynes climbing at a vertical speed ν cm./sec. is doing work against gravity at the rate of Wν × 10⁻⁷ W. This work must come (if the air is reasonably still) from the flight muscles. In addition, the muscles are doing work in churning up the air, and no doubt some is lost in heating up the not-quite-frictionless joints. However, it is certain that the pectoral muscles cannot be producing less power than Wν × 10⁻⁷ Was this is the amount which would be needed to account for the vertical speed if the wings were mechanically and aero dynamically perfectly efficient. If this power is called P_min, then the ratio P_max./P_min. gives a maximum value for the safety factor on tensile strength of the muscle insertions.

Feral Columba livia were used for the measurements made on dead specimens. These were trapped on city buildings in Bristol, and were kindly supplied to us by Mr M. K. Palfreman of the Ministry of Agriculture and Fisheries. Only adult birds were used, and, unless otherwise stated, measurements were taken as soon as possible after killing and dissection.

Rate of climb and wingbeat frequency were measured on tame pigeons kept on the laboratory roof.

The insertion of the pectoralis on the humerus was exposed, and the pigeon pegged down on its back with awls, with one wing projecting over the edge of the bench. One end of a piece of cotton was fixed into the muscle insertion, the other end being attached via a piece of elastic, to a clamp directly above the pigeon (Fig. 1). A pointer was attached to the cotton, and this moved over a scale as the humerus was moved up and down through its full travel. This method was used because the pectoralis insertion does not move in a straight line throughout its travel : when the humerus is elevated it moves in an arc, and this was automatically taken account of by the cotton wrapping round the curve of the shoulder joint.

Here the muscle was dissected away from its origin on the sternum, and the cotton was attached to the tendon near the anterior end of the muscle and in line with the direction of movement. The wing was then moved up and down and the movement of the tendon noted from a pointer on the cotton as before.

The humerus was dissected out with both muscles (as complete as possible for subsequent weighing) still attached to it. The humerus was rigidly supported, with the muscle whose insertion was to be tested downwards. A clamp was fixed to the muscle insertion, and from this a bucket was suspended (Fig. 2). Water was run into the bucket until the insertion broke. The bucket of water, with clamp and muscle still attached, was then weighed on a 20 kg. wt. spring balance. Care was taken to divert the stream of water as soon as the insertion broke, and to avoid loss of water by splashing. Errors from these causes were certainly within the 100 g. wt. nominal accuracy of the spring balance.

These measurements were made separately on each wing of each pigeon. The procedure differed somewhat as between the pectoralis and supracoracoideus muscles.

This muscle is very awkward for breaking tests, as it has a rather wide insertion on the deltoid crest which juts anteriorly from the proximal end of the humerus. The muscle inserts more or less directly on the bone, without any exposed length of tendon which can be gripped in a clamp.

The clamp used had two wedge-shaped jaws, which gripped the muscle insertion as close as possible to the humerus (Fig. 3). There was a tendency for the muscle to tear rather than break cleanly off at the insertion, and if this happened the reading was discarded. It was found easier to get a clean break between the clamp and the bone if the muscle was divided by a cut parallel to the direction of the applied force, into two approximately equal parts. These were than broken separately and the forces required to break the two halves were added together to give the total breaking force. Because of the difficulty of realistically simulating direct muscle pull on the insertion, readings obtained for the breaking strength of this insertion probably err on the low side.

This muscle converges to a parallel tendon about 1·2 cm. long which runs up to, and through the foramen triosseum, and inserts on the dorsal side of the humerus. This tendon is easily gripped in a clamp, and a clean break was reliably obtained between the clamp and the bone.

The clamp jaws had flat faces, which were notched to receive the tendon, in order to avoid crushing it. As with the pectoralis tests, the clamp jaws were lined with emery paper to give a better grip.

The results of the above four sets of measurements are set out in Table 1, together with the weights of the intact pigeons and the individual muscles.

Tame pigeons were fed by hand in the open on the flat roof of the laboratory in a corner of the 107 cm. high wall which surrounds the roof. A cine camera was set up level with the top of the wall, pointing into the corner. On the camera being started, a helper rushed at the pigeons, which were thus forced to make a near-vertical climb in order to get over the wall. The camera speed, nominally 48 ft./sec., was found to be 44·5 ft./sec. by filming a stopwatch, and measurements were made by counting frames on the film.

The fastest time regularly recorded for the climb to 107 cm. was 0·43 sec., giving a rate of climb of 250 cm./sec., which is taken as the maximum.

This was measured by counting frames for three complete wingbeat cycles. Six out of seventeen measurements came out at 8·9 cyc./sec., only one being faster than this, so this figure is used for the maximum wingbeat frequency.

The following are the definitions used for the various sorts of power output referred to in this section:

Average power output is the mechanical work done in one contraction divided by the time taken for one complete cycle of contraction and relaxation.

Peak power output is the work done in one contraction divided by the time taken for shortening.

Specific power output is power output per unit mass of muscle; either average or peak power outputs may be expressed in this way.

Using the averages at the bottom of Table 1 for breaking strengths and amplitudes of movement, the maximum amounts of work which conceivably could be done by each muscle in contraction are:

The muscles of both sides together could produce twice this, i.e. 5·38 joules per cycle. The maximum possible average power output at 8·9 cyc./sec. would thus be 5·38 × 8·9 = 48 W. It is not suggested that the flight muscles actually produce this amount of power—the conclusion is that they could not produce more than this without structural damage.

The average weight of the pigeons killed for dissection was 373 g.wt. Combining this with the above figure for maximum rate of climb, the flight muscles must be capable of producing at least 373 × 981 × 250 × 10⁻⁷ = 9·1 W at take-off. The safety factor on tension of the muscle insertions is thus not more than 48/9·1 = 5·2, and must in fact be considerably less than this.

Taking average weights for the two flight muscles from Table 1, the maximum possible power outputs per gram of muscle are: pectoralis, (2·48 × 8·9)/38 = 0·58 W/g.wt. supracoracoideus, (0·21 × 8·9)/6·7 = 0·28 W/g.

This discrepancy between the maximum possible average specific power outputs of the two muscles is somewhat puzzling, as the only substantial error at all likely to have been made, namely too low a figure for the breaking strength of the pectoralis insertion, would produce a discrepancy in the other direction.

The figures refer to average power output over a complete cycle of contraction and relaxation. Examination of the film showed that in vigorous flapping flight the upstroke is accomplished in about half the time needed for the downstroke—in other words the supracoracoideus spends about one third of the cycle in shortening and the other two thirds in being passively extended, while the reverse is true for the pectoralis. The maximum possible peak specific power outputs of the two muscles would therefore be about the same, namely about 0·86 W/g.wt.

The total weight of the flight muscles of both sides averaged 89 ·6 g. wt., so the minimum possible average specific power output for the flight muscles as a whole, derived from the rate of climb measurements, would be 9·1/89·6 = 0·10 W/g.wt.

In muscles which can exert the same force per unit cross-sectional area, and can shorten by the same proportion of their length, the power output per unit weight is proportional to the frequency of contraction. Thus small animals can produce more power per unit weight of muscle than large ones, because they can move their limbs more quickly (Hill, 1950). This fact needs to be borne in mind when comparing power outputs per unit weight of muscle in different animals.

Henderson & Haggard’s (1925) often-quoted figure of 0·017 W/g.wt. for the maximum sustained power output of the muscles of a rowing crew would presumably refer to a contraction frequency in the region of 0·5/sec., or one-eighteenth the maximum flapping frequency of the pigeon. Multiplying Henderson & Haggard’s figure by eighteen gives 0·31 W/g.wt., which is within the range found for the pectoralis above. Thus the high power output here deduced for pigeon flight muscle does not call for any unusual mechanical properties in the muscle, beyond an intrinsic speed of shortening appropriate to the size of the animal.

Where a muscle has a high sustained power output, this implies that suitable arrangements must exist for supplying it with fuel and oxygen, and for disposing of heat, at a corresponding rate. However, as the studies of George and co-workers (reviewed by George & Berger, 1966) on the flight muscles of birds clearly imply that the take-off performance of the pigeon would be based on anaerobic glycolysis, the figures deduced in the paper cannot be used to draw any conclusions about the respiratory system. The maximum sustained power could easily be below the minimum derived from rate of climb measurements, as the latter refers to short-duration ‘sprint’ performance, which can be maintained for periods of the order of 1 sec. during take-off or other strenuous manœuvres.

As both the flight muscles insert on the humerus, and have the major part of their origins on the sternum, their action tends to pull the shoulder joint towards the sternum. This is resisted by the coracoid, which acts as a compressive strut holding these two members apart. We measured the compressive strength of the coracoid in order to see how it compared with the tensile strengths of the muscle insertions.

The compressive load was applied in a simple caliper device (Fig. 4), the ends of the bone being embedded in Wood’s Metal (m.p. 70° C.) in order to distribute the load evenly. Three observations were obtained in which an abrupt compressive failure occurred in the central part of the bone, the forces applied at failure being 39·0, 44·1 and 43·4 kg. wt. (mean 42·4 kg. wt.). In the (seemingly improbable) event of both flight muscles contracting maximally at the same time, the maximum compressive load which could be applied to the coracoid would be 11·5 kg. wt. (from Table 1). The coracoid thus appears to be 3·7 times as strong as necessary to bear this load, and as we can see no other way in which it could be loaded in life, we are at a loss to account for this apparent excess of strength.

A study of the distribution of bending strength in the wing skeleton is deferred to a later paper, but since the entire bending moment derived from lift and drag forces on the wing is eventually concentrated on the pectoralis insertion, it is useful to obtain at this point an estimate of the maximum bending moment which can be transmitted by the pectoralis to the humerus.

The maximum force which can be applied by the pectoralis to the humerus has already been obtained, and it remains to determine the moment arm, i.e. the distance between the pectoralis insertion and the centre of rotation of the head of the humerus. As has already been pointed out, the pectoralis makes a very wide insertion on the deltoid crest, and we are obliged to make the somewhat crude assumption that its force acts through a point in the middle of this insertion, as was done in determining the distance through which the insertion moves in shortening.

By rigidly mounting the body of a dead pigeon in such a way that the wing could be moved through its full travel, it was found that the maximum angular excursion of the humerus was 142° (2·48 radians). Combining this with the observed distances of shortening of the two muscle insertions (from Table 1), their moment arms about the centre of rotation were obtained. Multiplying these by the breaking strengths gave the maximum bending moments. These figures are set out in Table 2.

The. force required to break the supracoracoideus tendon was converted into a tensile stress (force per unit area) by dividing by the cross-sectional area of the tendon. As this was awkward to measure directly, the mass m g.wt. of a length I cm. of tendon was found. The density d g.wt./c.c. of the tendon was then measured, thus allowing its volume ν c.c. to be obtained, since ν = m/d. The cross-sectional area a cm.² is now given by a = ν/l.

The density was determined by immersing a length of tendon about 1·2 cm. long in a mixture of chloroform and benzene, into which one or other of these substances was titrated until the specimen showed neutral buoyancy. The density of the mixture was then taken as equal to that of the specimen, and was calculated from the volumes of the two components.

The forces required to break the specimens were not determined separately, the average value of breaking force from Table 1 (2·62 kg. wt.) being used throughout. The results of four determinations are given in Table 3.

A similar method was used to determine the compressive stress needed to break the coracoid. A short (tubular) length was sawn from the hollow shaft of the bone, and its density found by flotation in a mixture of ethylene dibromide and ether, thus allowing the cross-sectional area of the cylindrical wall to be found. Table 4 gives the results of two determinations.