To fully understand what happens during a strike, we must first distinguish between two concepts that are almost always confused: momentum and energy.

When a fist strikes a target, it transfers both, but they do not have the same effects. Momentum is the product of mass and velocity, and it is this that pushes, unbalances, causes a head to pivot or a body to recoil. Energy, on the other hand, is proportional to mass but also to the square of the speed, and it is this that is expended locally in the area struck, where it causes bruising, cuts, fractures and pain. This difference has a very practical consequence. Doubling the speed of the fist multiplies its energy fourfold, whereas doubling its mass only multiplies it by two. There are therefore two main types of strike. Pushing strikes involve a great deal of mass at moderate speed, such as a straight knee in Muay Thai, and they displace the opponent, take the wind out of them and destabilise them.

Striking blows involve relatively little mass but a great deal of speed, and it is their energy that causes localised damage. The momentum of a strike cannot be cancelled out by a glove or foam padding, only by greater mass or by the target moving out of the way. Energy, on the other hand, is easily absorbed or dispersed by a compressible material or a larger contact surface. This is why a glove protects the tissues without preventing the head from being thrown backwards.

Added to this is a concept that explains everything else: impulse. Impulse is what a force transmits when it acts for a certain period of time, and it is equal to the momentum transmitted. The consequence is simple but decisive: to transmit the same amount of momentum, one can apply a small force for a long time or a large force very briefly. The average force during contact is therefore the momentum transferred divided by the duration of contact. Let’s take an example, using values I’ve made up for the sake of illustration. Imagine a fist carrying the equivalent of three kilograms behind it – that is, the hand, forearm, upper arm and part of the torso actually involved in the blow – travelling at nine metres per second, or around thirty kilometres per hour, which is entirely realistic for a trained striker. This blow carries a momentum of twenty-seven units and an energy of approximately one hundred and twenty joules. If the fist comes to a halt against the target in ten milliseconds, the average force reaches roughly two thousand seven hundred newtons, or approximately two hundred and seventy-five kilo-force. If it stops in five milliseconds, the force doubles. The duration of contact is therefore just as important as the speed, which explains why a blow that passes weakly through its target transmits less impact than one that comes to an abrupt halt.

We can take this a step further and ask what proportion of the energy actually remains in the target. In a soft-impact model, where the two masses move off together after contact, the energy dissipated as deformation is the initial energy multiplied by the ratio of the target’s mass to the sum of the two masses. For a head and neck weighing five kilograms struck by a fist with an effective mass of three kilograms, approximately sixty-two per cent of the energy is dissipated, amounting to nearly seventy-six joules. Against a forty-kilo heavy bag, over ninety per cent is absorbed, which explains why a bag does not behave like a head and why one cannot judge a strike solely by the way it moves a bag.

We must also dispel a persistent misconception: that of the mass behind a blow. A hand severed at the wrist would weigh around four hundred and fifty grams, which is less than one per cent of body weight. If we take an untrained fist thrown at ten or fifteen miles per hour, it would only be enough to set a head weighing four and a half kilos in motion at a speed of about one mile per hour. Even a fist travelling at twenty miles per hour, if it were on its own, would not push a head back by more than two or three miles per hour. To actually push someone back, therefore, one must commit far more than just the fist, and this is precisely what experienced strikers do; they manage to put up to around ten per cent of their body weight behind the strike, which is ten to twenty times more momentum than the fist alone. It is amusing to note that many practitioners claim to commit fifty to sixty per cent of their body mass to a technique.

This claim is not absurd in itself, as it describes the mass set in motion by the body during the movement, but it must not be confused with the mass actually transferred to the target during the few milliseconds of contact. Measurements taken from Olympic boxers striking an instrumented dummy show, on average, just under three kilograms of effective mass, for an average force of approximately three thousand four hundred and twenty-seven newtons and a hand speed of just over nine metres per second. What accounts for this difference in magnitude is precisely the structural integrity of the body at the moment of impact, a subject to which we shall return at length.

This suggests we should be wary of isolated figures for striking force that appear in magazines. The force of a blow is not a single number but a curve over time: a very brief initial peak, followed by a weaker tail as long as the striker continues to push. The value of the peak depends on the sensor’s sampling rate and the compressibility of the hand or glove, and it tells us almost nothing about either the energy or the momentum actually transferred. When we read that a strike is equivalent to a sledgehammer, or twice the force needed to fracture a skull, we are generally seeing a conflation of these concepts. Similarly, the spectacular figures cited in the world of karate – such as that of a small, 50-kilo practitioner supposedly measured at 2,000 pounds of force – are comparable only as an order of magnitude as long as the method, target and duration remain unknown. As for speeds, an untrained striker averages around five to seven metres per second, a professional between nine and eleven, and modern motion-capture measurements yield fist speeds of six to twelve metres per second depending on the level and type of strike. Some practitioners convince themselves that their strikes approach twice the speed of sound, whilst the actual measured values are around fifty times lower.

If the power does not come from the arm, where does it come from?

From the whole body, and more specifically from an orderly sequence of movements that biomechanics experts call the kinetic chain. An old principle of martial arts masters states that one does not strike with the fist but with the whole body, and modern science fully supports this view. In a straight punch from the rear arm, it all begins with the rear foot, which pushes against the ground, toes dug in. This push extends the ankle, then the knee and hip, and propels the pelvis forwards. The pelvis then rotates towards the target, with the rear hip literally snapping forwards. The torso follows with a slight delay, then the shoulder is brought forward, the elbow straightens, and finally the forearm rotates and the wrist locks just before impact. Each segment reaches its peak speed slightly after the previous one, then slows down as the next one takes over, with a time lag of a few tens of milliseconds between each link in the chain. It is this time lag that distinguishes a whipping strike from a strike delivered as a single, solid unit.

Several mechanisms explain why this chain of movement increases the speed of the fist. The first is the increase in the acceleration distance. The energy transmitted to the fist is the work done by the force that accelerates it; that is, this force multiplied by the distance over which it is applied. A novice who strikes using only their arm accelerates their fist only over the length of their arm. If they use their waist, this distance doubles, and if they initiate the movement from the driving foot, it triples. The longer the distance over which the force can be applied, the greater the final energy, provided that the acceleration is continuous: a link that slows down or seizes up breaks the chain. Chinese traditions compare this to a silk thread that snaps if one stops pulling it. The second mechanism is the addition of velocities. Think of a baseball pitcher standing on a moving lorry: as seen from the target, the ball’s speed is added to that of the lorry. In the body, the stride adds its speed to the pelvis, the pelvis to the shoulder, the shoulder to the arm, and these speeds accumulate for an observer standing opposite. The third mechanism is the whiplash effect. When a heavy segment transfers its energy to a lighter segment, the latter moves off much faster; the greater the mass ratio, the faster it goes. In the ideal case, with no energy loss whatsoever, the speed of the light segment is equal to that of the heavy segment multiplied by the square root of the mass ratio. If, for example, we imagine a torso and shoulder assembly weighing ten kilograms moving at three metres per second which transfers all its energy to an arm and hand assembly weighing two kilograms, the latter would travel at approximately six point seven metres per second. Reality is less generous due to energy losses, but the principle holds true and explains why a fist can move much faster than the pelvis driving it.

The non-striking arm also plays a role. Bringing the rear hand back towards the hip or chest increases the power of the strike, and this can be verified very simply by holding one arm outstretched without moving it whilst striking with the other: the loss of power is clear. Tradition explains this through Newton’s third law, with the withdrawing hand lending force to the striking arm. Mechanics, however, explains it in terms of rotation: positioning the opposite hand behind the body causes the shoulders to rotate, much like both hands on a steering wheel, which adds speed to the striking shoulder. The two descriptions are compatible, as the counter-rotation of the trailing arm increases the angular velocity of the torso and stabilises the axis, without it being necessary to imagine a literal transfer of force.

However, the chain must not remain loose right to the end. It must be fluid during acceleration, then become rigid on contact. For the body’s mass to be truly behind the fist, there must be a continuous rigid path between the fist and the centre of mass, located slightly below the navel. The ribcage is naturally rigid, but the abdomen is not, and this is why practitioners exhale or blow out at the moment of impact: the contraction of the diaphragm and the abdominal muscles provides the rigidity that was lacking. This principle is in line with that of so-called ‘reverse breathing’ in the Chinese internal arts, which I shall discuss later.

Martial traditions describe several ways of setting the body’s centre in motion to generate impact, and three of these relate primarily to the fist. The first is rotation, where the pelvis and waist rotate by approximately forty-five degrees as quickly as possible – as if throwing a ball – whilst the rear foot and leg push against the ground like a piston. The second is the thrust, which corresponds to the lunge strike: a sudden contraction of the adductors brings the rear leg sharply forwards, then the push from the rear foot delivers the strike. This is the strike that utilises the most body mass, but also the one that leaves one most vulnerable to losing balance. The third is the rise, used for the uppercut, in which the hips rise straight up with the punch, without fully straightening the legs and without lifting the chin. These angles of forty-five degrees or thirty degrees are instructional guidelines rather than fixed measurements: some boxing coaches, for example, recommend a hip rotation of nearly ninety degrees whilst stepping back for the hook, which serves as a reminder that the optimal range of motion depends on the punch, the distance and the boxer.

All of this is based on a fact that experienced boxers eventually come to feel in their feet: a punch delivered whilst standing cannot transmit more force than the ground and the body’s inertia allow to be countered. This is Newton’s third law applied to combat. When the fist pushes against the target, the target pushes back against the fist with an equal and opposite force, and this reaction must be absorbed by something: the ground, the body’s inertia or the striker’s joints. The universe does not choose who attacks. It expends energy in the easiest way possible. If the target is easier to compress or displace than you are, it is the target that bears the brunt. If you are poorly planted, you are pushed back. If the target is as rigid as a wall, it is your hand that takes the impact. A jumping kick, for example, generates momentum without a point of support, and when facing a well-planted opponent, it can happen that it is the striker’s own foot that cracks. If you are less stable than your opponent, you essentially absorb the greater part of the force of your own strike.

The sequence can be described in three stages: the force travels from the driving foot towards the target; the reaction travels back via the arm to the foot; and, if the footing is sound, a second wave travels back towards the target – what the traditions refer to as the ‘impact’. This image of the rebound is illustrative rather than precise, but it conveys an accurate principle: the harder the foot pushes against a stable surface, the more the torso and arm can rely on it at the moment of contact. During the prolonged push phase, the horizontal force that the feet can transmit is, moreover, limited by traction – that is, by the weight applied to the foot multiplied by the coefficient of friction between the shoe or the sole of the foot and the ground. A simple exercise allows you to feel this: standing on squares of cardboard, strike whilst pushing off with your back foot. If the cardboard slips under your foot, it means that the angle of push-off, the position of the foot or your stability need adjusting.

In a person standing upright, the ground reaction force is primarily vertical, and it is the rotation of the pelvis and trunk that converts it into a horizontal force directed towards the target. A kinetic analysis of a straight punch on a force platform has shown that the angular velocity of the torso increases as the reaction force under the front leg increases and that under the back leg decreases, with peak torso velocity occurring at impact, following the sequence: ankle, knee, hip, shoulder, elbow, fist. This qualifies the conventional view that only the back leg provides the thrust. Biomechanics experts describe the rear straight punch as follows: the rear leg extends and generates the propulsive force, then the front leg lands rigidly, producing a braking force and a horizontal torque on the pelvis, which is transmitted step by step up to the hand. In elite boxers executing a rear straight punch, the ground reaction force is distributed on average at 6.6 per cent on the front foot and 39.4 per cent on the back foot, compared with 54 per cent and 46 per cent in junior boxers. The front leg therefore acts as a pivot and a braking point.

A breakdown of the contributions to the power of the straight punch in advanced boxers, reported second-hand from an earlier study from the 1980s, gives approximately 38 per cent for the extension of the rear leg, 37 per cent for trunk rotation and only 24 per cent for arm extension. The exact breakdown varies depending on the punch and the boxer, but the order of magnitude is clear: nearly three-quarters of the power comes from the lower body and the torso, and only a quarter from the arm.

This gives rise to a few guidelines on footwork, which are found—with slight variations—in most boxing schools. The toes grip the ground and the weight is centred on the ball of the foot rather than on the heel or forefoot. The front knee remains directly above the toes without extending beyond them, with the shin as close to vertical as possible. The back knee is never locked, as a straight knee prevents the fighter from pushing and causes the impact to be absorbed by the joint. The rear heel remains on the ground when seeking maximum linear thrust, as a raised heel causes the ankle to absorb the reaction force. In boxing, by contrast, the rear heel lifts during rotation, with the body pivoting on the forefoot; this promotes pelvic rotation at the expense of a less direct linear thrust. Both strategies have their advantages, and one must not mix them without realising it. Finally, the stance must not be too low: a simple rule is that the buttocks should remain higher than the knees, as muscles that are stretched too far cannot contract quickly enough. Apart from that, the different stances each have their own uses.

The boxing stance, with weight slightly forward and the rear heel raised, offers mobility and good pelvic rotation. The Thai stance, which is more neutral, is suited to kicks and knees but weakens the punches. A side stance with seventy per cent of the weight on one leg facilitates evasion but is ill-suited to very powerful strikes. A long, forward stance, with most of the weight on the front leg, provides power and a low centre of gravity but reduces mobility. The short ‘cat’ stance prioritises mobility, whilst the ‘horse’ stance, with weight distributed evenly, prioritises lateral stability. To get a feel for all this, you can also push against a wall or a tree with the palm of your hand, keeping your back straight and without leaning your upper body forward: the harder you push, the more you feel the reaction travelling up your arm, through your shoulder and down your back leg right into your foot – and this is precisely the path a strike must follow.

That leaves the question of structure – that is, the way the bones are arranged to channel force without losing any of it. A force passing through a misaligned joint must be absorbed by muscles, which are neither strong enough nor fast enough to do so at the moment of impact. Boxers sum this up with a saying: where there is a joint, there is a weakness. The physical principle is that of the lever arm. When a force passes through a joint at a certain distance from its centre, it creates a moment that tends to bend it, and this moment is equal to the force multiplied by that distance. Let us imagine, again by way of example, an impact force of three thousand newtons acting two centimetres from the centre of the wrist: this creates a moment of sixty newton-metres, whilst the muscles of the wrist can counteract this by only a few tens of newton-metres at best, and in practice by only about ten. The wrist therefore gives way, absorbs the impact and becomes injured. When aligned with the axis of the forearm, the same wrist transmits the force almost exclusively as compression along the bones, which the bones can withstand very well. This is known as a ‘collapsed wrist’ when it is bent upwards or downwards on impact, and it is the same mechanism that explains, on a whole-body scale, why an elbow that is turned outwards allows force to escape, because the line of action of the reaction passes outside the joint and is dissipated through flexion.

This explains several guidelines concerning the fist itself. One strikes with the first two knuckles – those of the index and middle fingers – because the second and third metacarpals are almost immobile at the carpus and form a direct extension of the forearm, whilst the fourth and fifth are mobile and far more fragile. The knuckles are aimed at the shoulder, so that the force travels through the fist, wrist, elbow and shoulder in a straight line. The fist closes at the very last moment, as excessive tension in the wrist and forearm slows the movement, even though a clenched and stable fist prior to impact sustains fewer local injuries and fewer fractures. The elbow remains very slightly bent on impact, much like the knee in a kick, because a locked elbow reflects the reaction back into the joint and can cause it to hyperextend.

In the arm, three points relate more to mechanics than to tradition. A high-caged fist, at chest height, positions the elbow lower than the fist and isolates the pectoralis major, so that the strike relies solely on the strength of a single muscle. A fist caged at hip level, by contrast, places the elbow above the fist: the shoulder pushes through the elbow, and the elbow through the fist. An elbow turned outwards allows the arm to collapse under a partner’s push, whilst an elbow rolled downwards channels the force towards the rear foot. And the force only travels in a straight line from the arm to the rear foot if the hands and elbows remain in two parallel lines extending from the shoulders; joints bent at less than ninety degrees reduce the force.

The torso follows the same principle. Internal martial arts describe a very specific alignment: the head gently lifted with the chin slightly tucked in, the upper back rounded without slumping, the chest very slightly hollowed, and the tailbone drawn forwards and upwards. In mechanical terms, this amounts to maintaining the pelvis in a slight retroversion beneath a core that is engaged and stable on its vertical axis, without leaning either forwards or backwards. The exact angles described here are not derived from published measurements, but the principle is consistent with what boxing coaches refer to as an ‘engaged core’, capable of transmitting force. The body can, in fact, behave either as a single large rigid object or as a set of interconnected flexible parts, depending on the degree of muscle contraction. A rigid body transfers its entire mass to the punch but wastes energy and allows itself to be controlled by the limbs, whereas a relaxed body is difficult to grasp but fails to put its mass behind the punch. The correct approach is therefore time-dependent: supple during acceleration, rigid on contact. You can test your alignment with a partner, in a qualitative way: in a stable stance, with your fist extended, let your partner grasp your wrist and pull; you will find that you remain stable with your spine aligned, but that you are pulled forwards if you are leaning. The same test with the head tilted forwards or backwards shows that you are displaced much more easily. These tests are not quantitative, but they are reproducible, require no equipment, and very quickly reveal a flaw in power transfer.

Rotation is the most effective way of imparting speed to the fist, because a point situated far from the axis moves quickly even at a low rotational speed. The linear velocity of a point is its angular velocity multiplied by its distance from the axis. If, for the sake of example, we assume a rotation of the torso of ten radians per second – that is, approximately five hundred and seventy degrees per second – and a fist situated eighty centimetres from the body’s vertical axis, the fist already reaches eight metres per second through rotation alone, before the extension of the arm is added. Rotational inertia, on the other hand, depends on the square of the distance of the masses from the axis, which means that to accelerate the rotation of the torso quickly, it is advantageous to keep the arms close to the body at the start, then let them move away at the last moment. This rotation is produced by a torque arising from the legs’ push against the ground and the trunk muscles, and the angular acceleration is this torque divided by the inertia. The conservation of angular momentum completes the picture: when the front leg lands rigidly and slows the rotation of the pelvis, the angular momentum does not disappear; it is transferred to the lighter trunk and arms, which accelerate.

A crucial factor for power is that the pelvis must rotate towards the target whilst the upper torso is still turned in the opposite direction. This separation between the pelvis and shoulders stretches the trunk muscles, particularly the obliques, and brings into play what physiologists call the stretch-shortening cycle: the stored elastic energy and the stretch reflex reinforce the contraction that follows. This is exactly the opposite of the upper body rotating as a single unit, and martial arts traditions describe the same principle using their own terminology, instructing practitioners to rotate the hips and waist as quickly as possible, with the rear hip snapping forwards and the navel ending up facing the target. It is generally pointed out that too much rotation results in a push rather than an impact, but this is a teaching guideline rather than a measured threshold.

The arm itself acts as a lever, and a lever exchanges force for distance without ever generating energy. If the point of application moves twice as far away, the force at that point is half as great but the velocity is twice as high. The muscles attach very close to the joints, at the short end of the bony lever: they therefore exert a great deal of force over a short distance, and the hand, at the long end, moves much faster than the muscle contracts, with less force. The arm thus acts as a speed amplifier, which is precisely what we are aiming for, since energy increases with the square of the speed. This also explains why a strike delivered using only the arm is not very powerful: the arm’s lever, launched without the body’s momentum, has no reserve of energy behind it.

The geometry of the strike also plays a part. A wide circular punch covers a little over three times the distance of a straight punch, as the straight punch covers a radius whilst the curved punch describes a semicircle; and if we include the preparatory backward movement, the ratio rises to just over four. At equal fist speed, one could therefore throw four straight punches in the time it takes to deliver one wide punch, and eight if the straight punch travels twice as fast. This is why a wide punch is easily spotted and easily blocked. Circular punches do, however, have an advantage: their greater radius of rotation gives the fist a higher speed. Among elite boxers, the average speed is measured at eleven metres per second for the hook, ten for the uppercut and eight for the rear straight punch. For the hook and the uppercut, the shoulder accounts for the largest proportion of the segmental contribution, whilst for the back straight punch it is the elbow, with around thirty-nine per cent among elite boxers compared with twenty-seven per cent among juniors. Juniors rely too heavily on the shoulder in all their punches, a sign of less efficient energy transfer between the body segments.