How Spring Mechanics Work in Games

A spring is the simplest force in physics that is not constant. Push it further and it pushes back harder, in exact proportion. That one relationship — Hooke's law — turns out to underpin an enormous amount of game feel, from charge jumps to camera smoothing to the way a suspension system absorbs a landing.

The part that matters most in play is the squared relationship hiding inside it: force rises in proportion to compression, but stored **energy** rises with the square. Double the charge and you get roughly four times the height. This guide covers why, what damping does, and how springs appear in games that have no visible spring in them at all.

Hooke's law

The force a spring exerts is proportional to how far it has been displaced from its natural length, and it points back towards that length.

F = -k * x

Here x is the displacement and k is the spring constant — the stiffness. The minus sign is the whole character of a spring: the force always opposes the displacement, which is why a spring pushes when compressed and pulls when stretched.

A stiff spring has a high k. It resists more strongly for the same compression, stores more energy, and oscillates faster.

Stored energy and launch speed

The energy stored in a compressed spring is ½·k·x². When the spring releases, that energy becomes kinetic energy in whatever it launches: ½·m·v².

Setting those equal and rearranging gives the launch speed:

v = x * sqrt(k / m)

Three things follow, and all three are visible in play.

• Launch speed is proportional to compression. Double the compression, double the speed.
• Launch height is proportional to compression squared. Because height comes from energy, not speed. Double the compression, quadruple the height.
• Heavier objects launch more slowly from the same spring. The energy is fixed; spreading it over more mass gives less speed.

That table is the reason Spring Jump rewards commitment so heavily. A 50% charge does not get you halfway — it gets you a quarter of the way, and the rising floor does not wait.

Damping: why springs settle

An ideal spring never stops. Pull it and release it and it oscillates forever, converting energy back and forth between stored and kinetic indefinitely.

Real springs settle because of damping — a force proportional to velocity that opposes motion. The full model is:

F = -k * x - c * v

where c is the damping coefficient. The second term is doing the same job as friction, but in a way that depends on speed rather than on contact.

Three regimes

• Underdamped — the system oscillates with decreasing amplitude before settling. This is what most real springs do, and what looks 'springy' on screen.
• Critically damped — the system returns to rest as quickly as possible without overshooting. This is what you want for a camera or a UI animation.
• Overdamped — the system returns slowly without overshooting. Feels sluggish, but is occasionally right for heavy machinery.

Where springs show up in games

The visible ones are the least interesting use.

Charge mechanics

Hold to charge, release to launch. Spring Jump is the clearest example, and Planet Hopper uses the same structure for jumping between worlds. The squared energy relationship is what makes the charge decision interesting rather than a formality.

Bounce pads

A launch pad is a spring you do not control. It stores the energy of your arrival and returns it, sometimes with a bonus — which is a powered spring rather than a passive one.

Soft-body approximations

A grid of point masses connected by springs behaves like a deformable object. It is the classic way to simulate cloth, rope and jelly, and it is why those simulations tend to look wobbly when the damping is too low.

Suspension and landing

A vehicle's suspension is a spring-damper pair. So is the slight crouch a character makes on landing — usually not simulated, but animated to look like it is.

Constraint softening

Engines sometimes deliberately model a joint as a very stiff spring rather than a hard constraint, because a slightly soft joint is far more numerically stable than an exact one. The trade-off is visible sag.

Why stiff springs break simulations

There is a hard limit on how stiff a spring can be in a simulation with a fixed timestep, and exceeding it does not degrade gracefully — it explodes.

A spring oscillates at a frequency set by its stiffness and mass. If the simulation's timestep is longer than roughly a fifth of that oscillation period, each step overshoots further than the last, and the amplitude grows without limit until the numbers become infinite.

The three fixes

1. Reduce the stiffness. Often the correct answer. A softer spring that behaves is better than a stiff one that does not.
2. Reduce the timestep. Effective but expensive, since everything else runs more often too.
3. Use a constraint instead. If you want something rigid, model it as a positional constraint rather than as a stiff spring. That is exactly why Rope Swing uses a distance constraint rather than a very stiff spring.

The engine behind these games caps spring stiffness and runs at 120 simulation steps per second, which keeps the useful range of spring constants comfortably inside the stable region.

Playing spring games well

1. Commit to full charges. The squared energy relationship means partial charges are worth far less than they look. Two half charges are worth half of one full charge.
2. Charge immediately on landing. In any game with a rising floor or a timer, the time spent charging is time the hazard is gaining.
3. Look for free springs. Bounce pads give height without charge time. Routing to reach one is usually faster than charging twice.
4. Remember heavier launches slower. In games where you can affect your mass or carry something, the same spring gives less speed.
5. Aim before you charge. Once released, a spring launch is a projectile — you have spent your input and only small air steering remains.

• Tapping instead of holding. The most common error in charge games. A quick tap stores almost no energy at all, because energy goes with the square.
• Charging while a hazard approaches. Charge time is real time. If something is closing, a partial charge taken now often beats a full charge taken too late.
• Expecting to steer mid-launch. A spring launch is ballistic. Air control in these games is deliberately small.

Combining springs

Springs combine in a way that is exactly backwards from what most people guess, and getting it right matters for anything built from multiple spring elements.

In parallel — side by side

Two identical springs side by side share the load, so each is compressed half as much for the same force. The combined stiffness is the sum: two springs of stiffness k behave like a single spring of 2k. This is the intuitive case.

In series — end to end

Two identical springs end to end each carry the full load, so each compresses fully and the total compression doubles. The combined stiffness is halved. A longer spring is a softer spring, which is why a long rubber band stretches more easily than a short one cut from it.

Why this matters in simulation

A rope or cloth built from a chain of springs is effectively a series arrangement. Doubling the number of segments halves the effective stiffness, so a longer chain sags more unless you increase the per-segment stiffness to compensate.

That is a real trap when building soft-body systems: adding segments for visual quality quietly makes the whole structure floppier, and the usual fix — cranking the stiffness — pushes the simulation towards the instability threshold. Using iterative positional constraints instead sidesteps the problem entirely, which is why rope systems generally do.

Frequently asked questions

References