Power Screws: How a Car Jack Lifts a Tonne With One Hand

The first time you change a flat tyre, something feels wrong about the physics. You crank a thin little handle in slow circles, barely breaking a sweat, and a whole corner of a car — a quarter of a tonne or more — rises smoothly off the ground. Nothing about your effort feels like it should be enough. Yet it is, and it is repeatable, controllable, and safe enough to climb under.

The device doing the work is a power screw — a screw built not to hold parts together, but to move a load. Power screws sit inside car jacks, bench vices, clamps, valve stems, machine-tool tables, and the actuators that tilt solar panels and open theatre stages. Understanding one of them explains all of them, so let us take the humble screw jack apart and see exactly where its strength comes from.

A screw is a ramp you can never fall off

Imagine pushing a heavy crate up a loading ramp. A steep ramp is short but brutal; a long, gentle ramp lets you raise the same crate with far less push, because you spread the climb over a longer distance. That trade — more distance travelled for less force needed — is the entire principle of the inclined plane, one of the classical simple machines.

Now take that gentle ramp, made of something thin, and wrap it around a cylinder. The sloping edge traces a spiral up the rod called a helix, and the raised ridge it forms is the thread. A screw is nothing more than an inclined plane coiled around a shaft — but coiling it does something magical: the ramp now has no end. You can keep "climbing" it forever by turning, and the load can never slide back off the bottom the way a crate can roll off a real ramp.

Figure 1: Unwrap one turn of a thread and it is just a ramp. The base is the distance once around; the rise is how far the screw advances per turn.

Two measurements describe that ramp, and they matter for everything that follows. The pitch is the distance between neighbouring thread crests. The lead (symbol L) is how far the screw advances along its axis in one full turn. On a simple single-start thread the lead equals the pitch; on a multi-start thread — two or more separate helixes cut side by side — the lead is the pitch multiplied by the number of starts. Lead is the number that decides how fast the nut travels, so it is the one we track.

If you unroll one turn of the thread into a flat triangle, its base is the distance once around the screw and its height is the lead. The angle of that ramp is the lead angle (symbol λ), and it follows directly from the geometry:

tan λ = L / (π × dₘ)

Here dₘ is the mean diameter of the thread — roughly halfway between the outer crest and the inner root, because that is the average radius at which the thread surface actually pushes. A small lead angle means a long, gentle ramp: many turns to travel a little way, but very easy to turn. That gentleness is exactly what makes a jack feel effortless.

Square and ACME threads: built to push, not to grip

Look closely at a power screw and the thread does not look like the sharp V on a bolt. It is squared off or slightly trapezoidal. That is deliberate. A fastener thread is wedge-shaped to jam tight and resist loosening; a power-screw thread is meant to slide a load smoothly, so it uses a square thread or, more commonly, an ACME thread with gently sloped flanks (a 29-degree included angle in the inch system; the metric cousin is the trapezoidal Tr profile).

Square threads are the most efficient because their faces push straight along the axis with no sideways wedging, but they are hard to machine and cannot be adjusted for wear. ACME threads give up a little efficiency in exchange for being easy to cut, strong at the root, and compatible with a split nut that can be tightened as it wears. For most real machinery the ACME form wins, which is why a workshop lead screw or a vice spindle almost always carries it.

Where the strength comes from: the torque equation

To see why a small twist lifts a large load, balance the forces on our unwrapped ramp. The load W presses straight down. To raise it we push the thread sideways with a force P — this is the push your turning hand delivers at the thread surface. The ramp pushes back with a normal force, and because metal slides on metal there is also friction resisting the motion, set by the coefficient of friction μ between screw and nut.

Working through that force balance and then multiplying the rim push by the radius dₘ/2 to get a turning effort gives the standard raising torque for a power screw:

T = (W × dₘ / 2) × (tan λ + μ) / (1 − μ tan λ)

You do not have to memorise the algebra to read the meaning. The W × dₘ/2 piece says torque scales with the load and with how fat the screw is. The fraction is the friction-and-ramp penalty: the steeper the ramp (tan λ) and the stickier the surfaces (μ), the more torque each newton of load demands. Make the ramp gentle and the surfaces slippery, and the same load needs only a feather of effort. Lowering the load uses the same expression with the friction sign flipped, because now friction helps hold the load rather than resist the lift.

Figure 2: A screw jack. Turning the handle drives the screw through a fixed bronze nut, raising the load pad.

Worked example 1: a tyre-changing screw jack

Take a small bottle-style jack with a single-start ACME screw of mean diameter dₘ = 22 mm and lead L = 5 mm. The steel screw runs in a bronze nut with a coefficient of friction μ = 0.15. We want to lift one corner of a car carrying W = 1000 kg, which is a weight of about 9810 N. The crank handle is R = 250 mm long.

Step 1 — the lead angle

tan λ = 5 / (π × 22) = 5 / 69.1 = 0.0724, so λ = 4.1°. A very gentle ramp, as expected.

Step 2 — the torque on the screw

Numerator: tan λ + μ = 0.0724 + 0.15 = 0.2224.
Denominator: 1 − μ tan λ = 1 − 0.15 × 0.0724 = 0.9891.
W × dₘ/2 = 9810 × 0.011 = 107.9 N·m (using dₘ/2 = 11 mm = 0.011 m).
T = 107.9 × (0.2224 / 0.9891) = 107.9 × 0.2249 = 24.3 N·m.

Step 3 — the force on the handle

Spread that torque over the 250 mm handle: P = T / R = 24.3 / 0.25 = 97 N. That is about 10 kgf — a gentle one-handed pull. So a 10 kg push at the handle lifts a 1000 kg load. The mechanical advantage is roughly 9810 / 97 ≈ 100 to one. A tonne, lifted by one hand, exactly as the jack promised.

The trick is not free energy — it is the long spiral path. Your hand travels metres around the handle to raise the car a few millimetres, and that distance ratio is where the force multiplication hides.

Worked example 2: a workshop vice

A bench vice is the same machine clamping sideways instead of lifting up. Suppose its single-start square-thread spindle has dₘ = 18 mm, lead L = 4 mm, friction μ = 0.12 on a well-oiled steel-on-cast-iron pair, and a handle R = 150 mm long. You want a clamping force of W = 8000 N (about 800 kgf squeezing the workpiece).

tan λ = 4 / (π × 18) = 4 / 56.5 = 0.0708, so λ = 4.05°.
Numerator: 0.0708 + 0.12 = 0.1908; denominator: 1 − 0.12 × 0.0708 = 0.9915.
W × dₘ/2 = 8000 × 0.009 = 72 N·m.
T = 72 × (0.1908 / 0.9915) = 72 × 0.1925 = 13.9 N·m.
Handle force: P = 13.9 / 0.15 = 92 N, roughly 9 kgf.

So a 9 kg pull on the handle clamps with 8000 N — a mechanical advantage near 87. Notice how similar the two machines are despite doing different jobs: gentle lead angle, modest friction, a long handle, and the result is a hundred-fold boost in force.

Efficiency: the price of the trade

That huge force boost is not the whole story, because friction wastes a large slice of your effort as heat. Efficiency compares the work you actually deliver to the load against the work you put into the handle. For a power screw it comes out as:

e = tan λ / tan(λ + φ)

where φ is the friction angle, defined by tan φ = μ. For our jack, φ = arctan(0.15) = 8.5°, so e = tan(4.1°) / tan(12.6°) = 0.0724 / 0.224 ≈ 0.32. The jack is only about 32 percent efficient — two-thirds of your work is lost rubbing the threads together. The vice fares similarly at roughly 37 percent.

That sounds wasteful until you see what the inefficiency buys. Efficiency climbs steeply as the lead angle increases, peaking around 70 to 75 percent near a 40-degree lead and never quite reaching 100 percent. Steep, fast screws are efficient; gentle, strong screws are not. Designers of a jack deliberately choose the inefficient end, and the next section explains why.

Figure 3: Efficiency rises with lead angle. Jacks sit far to the left — low efficiency, but safely self-locking.

Self-locking: why the car does not crash back down

Here is the feature that makes a jack trustworthy. When you stop cranking, the load stays put. It does not unwind the screw and drop. A power screw with this behaviour is self-locking, and the condition for it is beautifully simple:

μ ≥ tan λ, equivalently the friction angle exceeds the lead angle (φ > λ).

In plain terms: if the ramp is gentler than friction can hold, the load cannot push its way back down. For our jack, μ = 0.15 comfortably exceeds tan λ = 0.072, so it locks and holds. This is precisely why jacks run such gentle lead angles and accept poor efficiency — a steep, efficient screw would be back-driveable, letting the load spin it down on its own the instant you let go. For lifting a car, holding the load safely matters far more than saving effort. A general rule of thumb: with typical dry-ish metal friction (μ around 0.1 to 0.15) any single-start screw with a lead angle under about 5 degrees will be self-locking.

The catches engineers watch for

Two practical points trip up the textbook picture. First, real jacks also rub where the rotating screw bears against the load pad or base — the collar or thrust face. Collar friction can add as much torque as the threads themselves, which is why good designs put a thrust bearing or a hardened washer there to cut it down. Our examples ignored it for clarity, so a real jack would need a little more handle force than we calculated.

Second, the failure modes are specific and worth knowing:

Failure mode	What happens	How designers prevent it
Galling / seizing	Steel-on-steel threads cold-weld and tear under load	Run a bronze nut against a steel screw; keep it greased
Thread wear	The softer nut slowly wears, adding backlash	Use a sacrificial bronze split nut you can adjust or replace
Buckling	A long screw in compression bows out sideways like a strut	Limit unsupported length; check it as a column
Thread shear / crushing	Threads strip if too few are engaged to carry the load	Engage enough nut length to spread the load over many threads
Overheating	Continuous fast travel cooks the lubricant	Switch to a ball screw or duty-cycle the motion

When raw efficiency matters — a CNC table that must move quickly and waste no motor power — engineers reach for a ball screw, which replaces sliding friction with recirculating balls and reaches 90 percent efficiency or more. But ball screws are not self-locking; they back-drive freely and need a brake to hold a load. The humble sliding power screw keeps its place precisely because its weakness, friction, is also its safety feature.

Engineering judgment: what to carry away

A power screw is a force amplifier whose gain you set with one number, the lead angle. Make it gentle and you get enormous mechanical advantage and automatic self-locking, at the cost of poor efficiency and slow travel — the right recipe for jacks, clamps, and valve stems that must hold position. Make it steep and you get speed and efficiency but lose the lock, which is fine when a motor and a brake are doing the work. The torque equation tells you the effort, the efficiency formula tells you the waste, and the self-locking condition tells you whether the load will stay where you left it. Get a feel for those three relationships and you can size, or sanity-check, almost any screw-driven mechanism on sight.

Power screws live in the same world as the threaded fasteners we cover elsewhere — the same helix geometry, the same friction physics, just aimed at moving loads instead of holding joints. If you want to keep building intuition for where torque, preload, and thread friction come from, our bolt pretension and torque calculator lets you turn these same ideas into numbers, and there is more in the same beginner-friendly series at enggtools.in/articles.