4.4 Mechanical Advantage, Velocity Ratio & Efficiency

Mechanical Advantage, Velocity Ratio & Efficiency

Maintenance work constantly multiplies force with simple machines: levers on hand tools, pulley blocks for lifting, jacks under the airframe, and ramps or wedges that raise loads gradually. Module 2 expects you to define mechanical advantage (MA), velocity ratio (VR), and efficiency, relate them by η = MA/VR, and recognise lever classes and common machines in SI energy terms.

Work In and Work Out

Work in mechanics is force times distance along the force (for constant force parallel to displacement):

W = F × s  (unit: joule, J = N·m)

For a machine:

• Work input = effort × distance moved by effort
• Work output = load × distance moved by load

An ideal frictionless machine conserves energy: work input = work output. Real machines always dissipate some energy (heat from friction, deformation), so:

work output < work input

That inequality is the seed of efficiency.

Mechanical Advantage (MA)

Mechanical advantage is the factor by which the machine multiplies force:

MA = load / effort = W / E

(Load and effort are forces in newtons.) MA is dimensionless. MA > 1 means the load exceeds the effort — you gain force. MA < 1 means you gain displacement or speed at the load end (Class 3 levers often do this) at the cost of a larger effort.

Actual MA uses the real effort needed including friction. Ideal MA (sometimes called theoretical) assumes no losses and is fixed by geometry alone.

Worked example. A jack raises a 12 000 N load with an effort of 400 N at the handle (actual).

MA = 12 000 / 400 = 30

The jack multiplies force by 30; you still pay with a long handle travel (next section).

Velocity Ratio (VR)

Velocity ratio (also called movement ratio) compares distances (or speeds) of effort and load:

VR = distance moved by effort / distance moved by load

VR is set by the geometry of the machine (lever arm lengths, number of rope segments supporting the load, ramp length versus height). For steady operation, the same ratio equals effort speed / load speed. VR is dimensionless and, for a given machine setting, does not depend on friction — friction changes the effort required (hence MA), not the ideal distance ratio.

Worked example. If the jack handle moves 0.60 m while the load rises 0.020 m:

VR = 0.60 / 0.020 = 30

Efficiency

Efficiency is useful work out divided by work put in:

η = work output / work input

With the definitions of MA and VR, and work = force × distance:

η = (load × distance_load) / (effort × distance_effort) = (load/effort) × (distance_load/distance_effort) = MA / VR

As a percentage: η% = (MA / VR) × 100%.

Because work output cannot exceed work input in a passive machine, η ≤ 1 (≤ 100%), and MA ≤ VR. Equality holds only in the ideal frictionless limit. If a calculation gives MA > VR, a definition or measurement was inconsistent.

Worked example — efficiency. Same jack: load 12 000 N, effort 400 N, VR = 30.

MA = 30, VR = 30 ⇒ η = 30/30 = 1.00 (100%) — idealised case.

If friction raises the required effort to 500 N: MA = 12 000/500 = 24, VR still 30, η = 24/30 = 0.80 (80%).

Work check: raise load 0.020 m ⇒ work out = 12 000 × 0.020 = 240 J. Effort moves 0.60 m at 500 N ⇒ work in = 300 J. η = 240/300 = 80%. Matches.

Levers — Three Classes

A lever is a rigid bar rotating about a fulcrum (pivot). Effort and load act at distances (perpendicular lever arms) from the fulcrum. Moments balance in the ideal static case: effort × effort arm = load × load arm, so:

ideal MA = effort arm / load arm

Class 1 — Fulcrum between effort and load

Examples: crowbar prying a nail (with pivot on the wood), scissors (double Class 1), pliers, many beam balances, see-saw. MA can be > 1 or < 1 depending on arm lengths. A long crowbar arm gives large MA for extracting fasteners or shifting heavy components.

Class 2 — Load between fulcrum and effort

Examples: wheelbarrow, bottle opener (some configurations), nutcracker, loaded sack truck. Effort arm is always longer than load arm, so MA > 1 always for a pure Class 2 geometry. Useful for lifting heavy packages onto stands with less effort.

Class 3 — Effort between fulcrum and load

Examples: tweezers, fishing rod, human forearm lifting a weight in the hand (elbow fulcrum), many tongs. Effort arm is shorter than load arm, so MA < 1 — you apply more force than the load, but the load moves farther/faster. Handy for fine control and speed of movement, not for force multiplication.

Worked example — Class 1 crowbar. Fulcrum 0.10 m from the load and 0.50 m from the effort. Ideal MA = 0.50/0.10 = 5. To crack a 2000 N load ideally needs 400 N effort; friction means somewhat more in practice.

Pulleys

A single fixed pulley changes the direction of the effort (pull down to lift up) with ideal MA ≈ 1. A movable pulley or block and tackle with n rope segments supporting the load has ideal MA ≈ n (and VR ≈ n). More string segments ⇒ higher MA ⇒ more rope to pull for the same lift height (VR rises with n).

Worked example. A block and tackle with 4 supporting strands lifts a 800 N load. Ideal effort = 800/4 = 200 N, VR = 4. If actual effort is 250 N, MA = 800/250 = 3.2, η = 3.2/4 = 80%.

Hangar use: lifting engines or components with chain hoists and pulley systems — always check SWL (safe working load) and never assume ideal MA when friction and sheave losses exist.

Inclined Plane

An inclined plane (ramp) raises a load of weight W through height h by sliding it along length L at angle θ to the horizontal (sin θ = h/L).

Ideal effort (frictionless, push parallel to slope) = W sin θ, so:

ideal MA = W / E = 1 / sin θ = L / h

VR for a full climb is also L/h in the ideal distance sense. A gentler ramp (small θ, large L/h) needs less effort but more travel — same energy trade-off as other machines.

Worked example. Load weight 1000 N, ramp length 5.0 m, height 1.0 m. Ideal MA = 5.0/1.0 = 5, ideal effort = 200 N. If actual effort is 250 N, MA = 4, η = 4/5 = 80%.

Wedges and screw jacks are inclined-plane variants (the screw is an inclined plane wrapped around a cylinder); the same MA/VR/efficiency language applies.

Tool and Jack Applications on Aircraft

• Hydraulic jacks use fluid pressure (Chapter 3 pressure ideas) but still obey energy accounting: pump handle travel × force relates to ram force × ram travel via MA/VR and losses.
• Torque wrenches and long-handled tools are lever applications — longer handle, larger moment for the same hand force (watch fastener torque limits).
• Cable and pulley control runs reverse direction and can arrange mechanical advantage in older systems; modern powered controls still rest on the same statics and work principles.
• Ramps and dollies move heavy units with inclined-plane advantage.

Safety note: high MA means a small effort can move a large load — but the load can also move you if the machine runs away; chock, stay clear of pinch points, and never exceed rated capacities.

Definition Sheet

Simple machines never give “something for nothing”: what you gain in force you pay in distance (and a bit more for friction). Keep MA, VR, and η linked through work, and classify levers by fulcrum–load–effort order — that is the Module 2 core for this topic.