Efficiency Testing

Part of Simple Machines

How to measure the real-world efficiency of machines and identify where energy is being lost to friction.

Why This Matters

Theoretical mechanical advantage tells you the maximum force multiplication a machine can provide. Real-world efficiency tells you how much of that theoretical advantage you actually get. The difference is friction — unavoidable in all physical machines, but highly variable depending on design quality, lubrication, and wear.

Efficiency testing is not academic. When you build a water mill and find it produces only 40% of the power you expected, efficiency testing tells you whether the problem is in the millstone bearing, the gear mesh, or the wheel paddles. When your block and tackle requires twice as much pull as the calculations say, efficiency testing locates the specific pulleys that are absorbing energy. Without this diagnostic capability, you can only guess at improvements.

More broadly, measuring the efficiency of your machines creates a feedback loop for improvement. You build a machine, measure its efficiency, identify the lossy components, improve them, and measure again. Over time, this systematic approach produces significantly better machines than trial-and-error without measurement. It is the difference between engineering and tinkering.

What Efficiency Means

Efficiency is the ratio of useful output work to total input work:

Efficiency = Output Work / Input Work × 100%

Work = Force × Distance. So:

Efficiency = (Output Force × Output Distance) / (Input Force × Input Distance) × 100%

For a simple lever:

• Output: the load lifted (kg) × the distance lifted (m)
• Input: the force you applied (kg) × the distance your hand moved (m)

A perfect machine (100% efficiency) converts all input work to output work. Real machines always have losses, primarily from friction at bearings, between gear teeth, in rope-pulley contact, and in structural deformation.

Typical efficiencies by machine type:

Machine	Typical Efficiency	Main Losses
Well-greased iron pulley	90-95%	Bearing friction
Wooden pulley, greased	75-85%	Bearing + groove friction
Wooden pulley, dry	60-75%	High friction
Wooden gears, greased	80-90% per stage	Tooth profile errors
Rope through ring (no wheel)	50-70%	High rope-ring friction
Screw jack, metal threads	20-50%	Thread friction (by design)
Block and tackle (4 pulleys)	60-75% total	4 pulley losses in series

Measuring Input and Output

To test efficiency, you need to measure both input force and output force (or input work and output work).

Measuring Force Without a Scale

If you do not have a calibrated scale, you can create reference weights:

• A known volume of water (1 liter = exactly 1 kg)
• A container of precisely measured grain (weighed against water)
• A set of standardized stone or iron weights calibrated against water

Simple balance scale: A rigid bar suspended at its center, with hooks at each end. When loads at both ends are equal, the bar is horizontal. This allows direct comparison of unknown forces against known weights.

Spring scale (simple version): A known-length spring stretches proportionally to force applied (Hooke’s Law). Measure the stretch of a consistent spring under known loads to create a calibration chart. Then measure stretch under unknown forces to determine the force.

A spring can be made from a hardwood strip or a bent green branch — though metal springs are more consistent.

Measuring Distance

For pulling and lifting, distance measurement is straightforward: mark the rope or measure with a cord before and after the movement.

For rotary motion (measuring distance at the circumference of a wheel): mark a spot on the wheel, count rotations, multiply by the circumference (π × diameter). Or measure directly with a cord wrapped around the circumference.

Practical Efficiency Tests

Testing a Single Pulley

Setup:

1. Mount a single pulley (fixed) overhead
2. Hang a known weight (load) on one end of a rope through the pulley
3. Measure the force required to lift the load slowly (constant velocity) by pulling the other end
4. For a frictionless pulley, you would pull exactly the load weight (1:1 MA, no force advantage, but direction change)

Calculation:

Efficiency = Load Weight / Measured Pull Force × 100%

If the load is 50 kg and you need 55 kg of pull to lift it slowly: Efficiency = 50/55 × 100% = 91%

The 9% loss is friction in the pulley bearing. Compare this same pulley before and after greasing — typically 10-20 percentage point improvement from good lubrication.

Testing a Block and Tackle

Setup:

1. Attach the fixed block to an overhead support
2. Hang a known load on the movable block
3. Pull the hauling end at a slow, constant velocity
4. Measure the pull force with your spring scale or balance

Theoretical force (no friction):

Theoretical pull = Load / Number of rope segments

For a 4:1 tackle with 100 kg load: Theoretical pull = 25 kg

If actual pull is 35 kg:

Efficiency = 25 / 35 × 100% = 71%

Identifying the loss source: Test each pulley individually to find which one is causing the most friction. Replace its axle pin, check the groove for wear, regrease, and retest.

Testing Gears

Setup:

1. Mount the gear pair with shafts turning in their bearings
2. Apply a known torque (twist force) to the input shaft
3. Measure the output torque

Measuring torque without instruments:

• Apply a known force at a known radius from the shaft center
• Torque = Force × Radius
• For an input gear with a 15 cm radius handle: applying 10 kg at the handle = 1.5 kg⋅m torque input

Calculation: If input torque is 1.5 kg⋅m and output torque (measured with the same method on the output shaft) is 2.7 kg⋅m, with a 2:1 gear ratio (output shaft turns twice as slow):

Theoretical output torque = 1.5 × 2 = 3.0 kg⋅m
Actual output torque = 2.7 kg⋅m
Efficiency = 2.7 / 3.0 × 100% = 90%

Testing a Screw Press

Screws have inherently lower efficiency because the thread friction is very high (this is what allows them to hold position without a ratchet). However, you can still measure it.

Setup:

1. Apply a known force to the lever handle
2. Measure the force the press platen exerts using a test block and a spring scale or lever balance

Calculate:

Theoretical output force = Input Force × (2π × lever radius / thread pitch)
Measured output force = (from your measurement)
Efficiency = Measured / Theoretical × 100%

Typical screw press efficiency: 20-40% (most energy goes to thread friction, which also provides the self-locking property).

Systematic Improvement Process

Once you have baseline efficiency measurements, follow this improvement cycle:

1. Identify the highest-friction component. In a multi-stage system, the component with the worst individual efficiency contributes most to total losses. Test each stage individually.

2. Lubricate first. Add lubrication before making any mechanical changes. Lubrication is free (or nearly so) and often improves efficiency by 15-25 percentage points.

3. Check bearing fit. Too-tight bearings generate more friction than slightly loose ones. The bearing clearance should be 1-2 mm (tight enough to run true, loose enough to not bind).

4. Check surface quality. Rough bearing surfaces (file marks, splinters, tool marks) increase friction. Smooth surfaces with a plane, file, and sandstone (or whetstone).

5. Retest after each change. Change only one variable at a time. This tells you which change provided the benefit. If you change three things at once, you cannot tell which improvement was responsible.

6. Document results. Record the efficiency before and after each change. This creates a history that shows the value of specific improvements and guides future work.

The 80% Rule

In most machines, 80% of the friction loss comes from 20% of the components. Finding and fixing those high-friction components gives most of the possible improvement with minimal work. Do not spend equal effort on every bearing when one or two are clearly the worst offenders.