The one number that actually matters

Every archer knows a bow's peak weight. Sixty pounds. Seventy pounds. That number is stamped on the limb, quoted in the specifications, and used in every conversation about draw weight. It is also, by itself, almost useless for predicting arrow speed.

The number that actually determines how much energy the arrow carries is not the peak weight of the bow. It is the integrated area under the draw-force curve — the total work done by the archer as the string moves from brace to full draw. That area is the potential energy stored in the limbs, and it is what gets released back into the arrow at the shot. Two bows with identical peak weights can store dramatically different amounts of energy, and dramatically different amounts of energy launch dramatically different arrows.

Peak weight is what the archer feels. Stored energy is what the arrow gets.

This distinction is what makes the compound bow, as a machine, interesting. A compound is a design that maximizes the ratio of stored energy to peak draw weight — that stores more energy per pound of peak load than any other bow. It accomplishes that by shaping the draw-force curve deliberately, using the geometry of a rotating cam to raise force where force is easy to apply and lower it where force is hard to hold.

Figure 1 — Draw-force curves compared Overlay of three draw-force curves on the same axes (draw length vs. force): (a) longbow — near-linear ramp; (b) recurve — linear-with-slight-stack; (c) modern compound — steep ramp to peak, plateau, valley to holding weight. Shaded area under each curve equals stored energy. The compound curve encloses more area for the same peak weight — that extra area is where the compound's speed advantage lives.

The recurve baseline

Start with a recurve, because it is the honest baseline against which the compound is doing something clever. A recurve's draw-force curve is close to linear: the further the string is drawn, the more force is required to draw it further. Not perfectly linear — the limbs behave slightly differently near the brace and near the wall — but close enough that the area under the curve is roughly a triangle. That triangle is the stored energy.

For a recurve peaking at 45 pounds at 28 inches of draw, the stored energy is approximately one-half times the peak force times the draw distance — around 55 foot-pounds. And crucially, the archer is holding that full 45 pounds at the moment of release. There is no let-off. Every pound of peak weight is a pound the archer is fighting the entire time they aim.

A recurve is a mechanically simple machine. Its integration efficiency — the ratio of stored energy to peak weight times draw length — is bounded by geometry to somewhere around 50 percent. That is the number the compound cam exists to beat.

What a cam actually does

A compound cam is a rigid wheel with two things going on: the bow's main string is attached to it at one point, and the buss cable (or the control cable, or the yoke — the terminology varies) is attached to it at another point. As the archer draws the string, the cam rotates. That rotation simultaneously plays out string on one side of the cam and takes up cable on the other.

The critical fact is that the string and the cable are attached to the cam at different distances from the cam's axle. Those distances are called the effective radii, and they are what determines how much force it takes to rotate the cam at any given moment.

The mechanical advantage of a cam is the ratio of those two effective radii. If the string pulls on the cam at a radius of 2 inches from the axle, and the cable pulls on the cam at a radius of 1 inch from the axle, then a 20-pound pull on the string generates 40 pounds of pull on the cable — the cam is acting as a 2:1 lever. Conversely, if the cable is being pulled by the limb tip with 100 pounds of force, the string only has to be held with 50 pounds to keep the cam from rotating.

Figure 2 — Cam as a variable lever Cross-section of a modern compound cam showing: (a) string groove and its instantaneous effective radius Rs; (b) cable groove and its instantaneous effective radius Rc; (c) the axle. Arrows indicate directions of string pull and cable pull. Annotation shows mechanical advantage MA = Rc / Rs at that cam angle. Both radii change as the cam rotates. That is the entire trick.

Neither radius is constant. Both the string groove and the cable groove trace non-circular paths around the cam's axle. As the cam rotates through the draw cycle, those effective radii change continuously. Which means the mechanical advantage changes continuously. Which means the force required to hold the string at any given draw position changes continuously — and can be shaped, by the cam designer, into whatever draw-force curve the design calls for.

The cam is a lever whose fulcrum moves as it turns.

Shaping the curve

Now the interesting part. A cam designer looking at a compound draw cycle wants three things, in order:

  1. Ramp quickly to peak weight during the first third of the draw, so that the archer is doing hard work early — where their leverage on the bow is best.
  2. Hold at peak weight through the middle third of the draw, so that energy is being stored continuously into the limbs across the maximum practical distance.
  3. Drop sharply to holding weight in the final third, so that when the archer reaches the back wall, they are holding only a fraction of peak.

To achieve each of these behaviors, the designer arranges the effective radii of the string groove and the cable groove so that their ratio traces the desired mechanical-advantage curve as the cam rotates.

During the ramp phase, the string groove's effective radius is small relative to the cable groove's — mechanical advantage is low, and every inch of string movement demands high force. Peak weight is reached quickly.

During the plateau, the two radii are arranged such that the ratio stays approximately constant even as the cam continues to rotate. The archer feels no change in force through this section, but the limbs are being progressively loaded. This is where the compound stores its energy, and it is why the compound's draw-force curve encloses more area than a recurve's for the same peak weight.

Then, in the final third of the draw, the geometry crosses over. The string groove's effective radius grows sharply, while the cable groove's effective radius stays roughly the same or shrinks. Mechanical advantage rises rapidly. The force on the string drops away. This is the let-off. The archer settles into the valley, holding the wall against a weight that may be only 15 to 25 percent of what the limbs are still storing.

Figure 3 — How cam profile shapes the draw-force curve Left: outline of a modern compound cam showing the string groove and cable groove tracks. Right: draw-force curve annotated with the ramp, plateau, transition, and valley phases. Callouts connect specific angular sections of the cam (α, β, γ, δ) to their corresponding regions on the draw-force curve. Every feature of the draw feel — the ramp, the wall, the valley — is a decision made in the cam's outline.

Let-off, precisely

Let-off is often stated as a single number: 80 percent, 85 percent, 90 percent. That number is the fraction of the peak weight that has been "let off" at the wall. A 70-pound bow with 85 percent let-off is holding 10.5 pounds at full draw. The other 59.5 pounds are still being stored in the limbs, waiting to launch the arrow.

The mechanism producing that let-off is the ratio between the cam's mechanical advantage at peak and its mechanical advantage at the wall. If the cam's MA at peak is 1:1 and its MA at the wall is 7:1, then a 70-pound limb force produces 70 pounds on the string at peak and 10 pounds on the string at the wall. That is 85.7 percent let-off, generated entirely by cam geometry. No springs, no ratchets, no clutches. Just the same lever principle a child uses on a seesaw, applied through a shape rotating around an axle.

Let-off is not a feature added to the bow. It is the geometric consequence of the cam having a much longer effective lever arm on the string groove at full draw than at peak. Every compound has let-off. What varies is how much and how it is shaped.

The control cable is not a bystander

Here is the part that most treatments of cam mechanics skip. The buss cable — the "control cable" — is not passive. It is the cam's other input. The cam does not know how far the archer has drawn the string; it only knows the angular position it has been rotated to. That angular position is determined jointly by the string being drawn out and the cable being played in. Both actions must happen in coordinated proportion, or the cam will not reach the intended full-draw position at the intended draw length.

This is why the control cable's length is not a rough number. It is the single parameter that determines where the cam sits at every point in the draw cycle. Change the cable length by even a small amount — on the order of an eighth of an inch is enough — and the cam's rotational position shifts noticeably. That shifts the effective radii, which shifts the draw-force curve, which shifts everything downstream: peak weight, let-off, valley aggressiveness, and the position at which the wall is felt.

Figure 4 — Control cable geometry and its effect on the DFC Diagram of a bow at full draw showing: (a) the string path from cam to nocking point; (b) the buss cable path from top cam through the yoke to the bottom cam attachment (or, on hybrid systems, cable-to-cam paths on each side); (c) the roller guard or cable slide constraining lateral cable position. Below: a family of three DFCs on the same axes, corresponding to nominal cable length, cable length 1/8" long, and cable length 1/8" short. A small change in cable length is not a small change in the draw-force curve. It is a whole-curve shift.

Modern two-cam compounds have a further wrinkle: the two cams must reach their intended angular positions in synchronization. Even a couple of degrees of mismatch between the top and bottom cams at full draw is enough for both cams to have effective radii slightly different from what the design specifies, and the arrow experiences slightly asymmetric launch forces — one limb releasing marginally sooner than the other. This is what "timing" means in compound tuning, and it is why the control cable length on each side (or the buss cable length between the two cams) has to be set with the same precision as the main string.

The tradeoffs the cam designer makes

A cam can store more energy per pound of peak weight, but the tradeoff shows up in feel. The most efficient cam profiles — the ones that store the most energy for the same peak — tend to have aggressive valleys and short, hard walls. The bow feels fast because it is fast, but it is also less forgiving of a shooter creeping forward off the wall during the shot.

Smoother cams sacrifice some integration area — a percentage or two of stored energy — in exchange for a longer, more forgiving valley. The archer who creeps forward on the shot experiences a smaller force spike, and the shot is less punished for imperfect back tension. These are called "smooth-draw" cams, and they are why some target archers prefer them despite the small speed penalty.

Neither is wrong. They are different points on a Pareto frontier of stored-energy-per-pound-peak versus draw-cycle forgiveness. The cam designer picks a point on that frontier and shapes the string and cable grooves to hit it. The archer picks a bow whose cam sits at the point they want.

There is no perfect cam. There is only the cam that matches how the shot is going to be executed.

What this means for the string builder

Every geometric relationship described above depends on the bow's string and cables having exactly the lengths they were designed to have. The manufacturer specifies a bus/control cable length and a main string length to the nearest sixteenth of an inch, and those specifications are not conservative guidance — they are the geometric input parameters of a mechanical system whose behavior changes measurably when the inputs change.

A string that stretches — mechanism one from Creep vs. Stretch — is a string whose length is drifting away from the manufacturer's spec. As the length drifts, the cam's angular position at every point in the draw shifts. Peak weight moves. The valley moves. Timing shifts. Every symptom the archer perceives as a "tuning issue" is downstream of a string that is no longer the length the cam designer assumed it would be.

This is the whole reason a well-tensioned, well-burnished, fully-stretched string matters. The cam does not tolerate length drift. The archer feels the drift as everything getting slightly worse over time. The string builder's job is to deliver a string whose length will not drift measurably across the life of the bow's tune.

Why the bench matters. The cam's whole design depends on the string being the exact length the designer specified. A string that stretches is a bow that de-tunes itself. A stable string is the precondition for every other tuning operation working as intended.

The elegance of the machine

A compound bow is a device that lets a human hold ten pounds at full draw and still store the energy of a sixty-pound bow. It accomplishes this without motors, without gears, without any active component. It is a shape rotating around an axle, with two strings attached at carefully chosen points, held together by carefully chosen lengths. Every property of its behavior — peak, valley, let-off, timing, sound, speed — is a geometric consequence of those choices.

The physics of it was worked out over the course of a few decades in the mid-20th century, refined in patents that most modern archers have never read. What the archer experiences as the feel of a bow is, underneath, the elegant meshing of Archimedes' lever with the calculus of a non-circular pulley. The string builder's contribution to that machine is a single input: the lengths. Get the lengths right, and the machine works. Get them wrong, and no amount of tuning downstream will make the machine work.

The compound bow is a proof, in wood and aluminum, that Archimedes was right about levers.

Connections

See The helix for why a bowstring is not a passive object. See Tension and dwell for how the bench delivers a string at the specified length. See Creep vs. stretch for the mechanisms that make a string drift away from that length, and what to do about each.

← Creep vs. stretch  ·  Science & Mechanics

Published 2026-07-04  ·  Axial Bowstrings