The Resistance Curve
Unreasonable demands
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The resistance curve refers to variations of resistance that occur as a weight moves through an arc. This is the result of the moment arm lengthening or shortening, increasing or decreasing the demand placed on the muscle while the actual weight or mass of the load remains unchanged.
If much of the following explanation of the resistance curve sounds similar to my previous piece on moment arms, it's because the two phenomena are intertwined. Both are fairly simple concepts but are crucial to mastering the mechanics of movement, and can become quite complex when accounting for multiple bones, joints, and muscles during full body movements.
When you hold a ten pound dumbbell out to the side so that your arm is parallel to the floor, you're not just resisting the ten pounds of the dumbbell. You're resisting the the ten pound dumbbell multiplied by the length of your arm.
If you raise or lower your arm by 45 degrees, you're shortening the moment arm (by reducing the horizontal distance). The moment arm is measured perpendicular to the direction of resistance—in this case gravity.
The force required to resist the weight of the dumbbell decreases, because the moment arm has decreased. Meanwhile the weight of the dumbbell has remained the same because Earth's gravity hasn't changed.
However, you will find it harder to resist the dumbbell at 135 degrees (45 degrees above parallel) than at 45 degrees (below parallel). This is because of the strength curve of your deltoids, which are in a shorter position when your upper arm is above parallel to the ground.
Remember the strength curve of a muscle dictates that the muscle will be at its weakest when in its shortest position.
In this example, your lateral deltoids reach their shortest position somewhere between 60 degrees and 90 degrees of shoulder abduction, depending on your individual anatomy. As you continue to bring your arm overhead, your shoulder blade has to rotate upward to make room for your upper arm bone to reach a vertical position.
So from 90 degrees to 180 degrees, your lateral deltoid is essentially doing an isometric hold in its shortest position, and your trapezius muscle is pulling your arm overhead the rest of the way by rotating your scapula.
Your lateral deltoid is at the weakest point of its strength curve at 90 degrees, while the resistance curve of the motion is at its most challenging.
This is why some exercises feel disproportionately hard at one specific point, rather than uniformly hard throughout — the resistance curve and the strength curve are working against each other at exactly the joint angle where it matters most.
The ideal exercises for muscle development will have a resistance curve that aligns with the associated muscle's strength curve. Meaning that as the strength curve of the muscle reaches its weakest point, the resistance curve of the exercise will drop off accordingly.
Complicated Arcs
A golf swing involves the same principle operating across multiple joints simultaneously, at speed, with no opportunity to pause and recalibrate.
On the backswing, the hips, arms and club rotate away from the ball. The horizontal distance between the clubhead and the body's rotational axis is relatively short at address, lengthens as the club moves away, and reaches its longest point at the top of the backswing. The resistance curve is climbing through this phase — the load on the muscles controlling the arc is increasing as the club moves further from center.
At the transition, the direction reverses. The downswing begins proximal to the rotational axis and works outward — hips first, then torso, shoulders, arms, and finally the club — each segment accelerating the next in sequence. This is the movement pattern that generates clubhead speed. It is also the phase where the resistance curve is at its most demanding, because the clubhead is traveling the longest arc at the highest velocity, and the moment arm is near its maximum through the release.
At impact the geometry either lines up or it doesn't. The window where the resistance curve and the muscles' available force actually correspond is narrow, and unlike a bicep curl, there is no slowing down to find it. The club is accelerating through impact and the body has already committed.
The positions that feel hardest in a golf swing are the positions where the resistance curve is highest and the margin for mechanical error is smallest.
The concept of “load” and “resistance” here can seem counterintuitive. We're not digging ditches in the permafrost. The weight of a golf club is negligible. Golf is light, fast, and technically precise, and the demand is invisible until something breaks down. The cumulative mechanical load of 70 to 100 swings, each one asking specific muscles to produce force at specific points in a long-lever arc, adds up to something real — it just doesn't announce itself the way a heavy load does.
Which is why we can feel fine after a round but then can't figure out why our performance is degrading over a season. The initial demand may not be obvious, but over time the accumulation is.
Not all Curves are Resistance Curves
For a motion to have a resistance curve there must be a fixed direction of resistance. In both the lateral raise and golf swing examples above, the active lever or moment arm rotates through a fixed line of action.
Put another way, a resistance curve exists when a fixed-direction force and a rotating lever interact. When the angle between them changes, the demand changes.
At a surface level, rowing appears to have a resistance curve. There are two obvious levers—the oars—that trace graceful arcs. Force and resistance are being generated by and against the water. There is a clear and simple geometry in motion.
In spite of all this, rowing a boat in the water does not have a resistance curve because there is no fixed direction of resistance. The resistance of the water is generated by the action of the blade: action and then reaction, and scales with the effort of the rower as opposed to gravity, whose pull on a given mass is constant regardless of velocity.
The moment arm of the oar—the distance from the blade to the pin, measured perpendicular to the direction of resistance—is a fixed length. But the water's resistance against the blade will always be perpendicular to the blade, regardless of the angle of the oar relative to the hull or keel of the boat.
Since the length of the oar is fixed, and the blade travels in an arc, and the resistance generated by the water is always opposite to the blade, the moment to the axis is always the same length. Hence, no resistance curve.
Without a fixed direction of resistance, the demand in rowing is solely the product of the rower's own force output. The water mirrors whatever its given, which means the most demanding parts of the stroke are wherever the rower's own strength curve is weakest—the catch and the finish, where the relevant muscles are nearest their end range. Producing even force through these positions, rather than backing off, is where the rower's effort can outrun what the tissue can deliver and where injury is most likely to occur.
Which brings us to the most actionable part of both the resistance curve and the strength curve. It's typically not feasible to alter the mechanical demands of a given sport or activity so that both curves align in an ideal way to prevent or reduce injury to the muscles and joints. But understanding the principle of aligning the resistance and strength curves for any complimentary training and rehab outside of said sport or activity will go a long way toward improving longevity and recovery.
