A control valve actuator must generate enough force or torque to move the valve through its full travel against all opposing forces: process pressure acting on the closure element, packing friction, seat friction, and any dynamic forces from flowing fluid. An undersized actuator stalls or fails to seat, causing leakage and loss of control. An oversized actuator wastes air, adds unnecessary weight and cost, and may damage valve seats by applying excessive seating force.
The actuator sizing process starts with calculating the total required torque or thrust, adding a safety factor, and then selecting an actuator that delivers at least that torque at the minimum expected supply pressure. For spring-return (fail-safe) actuators, the calculation must also verify that the spring can close (or open) the valve against worst-case process conditions with zero air supply.
This guide covers torque calculations for butterfly, ball, globe, and plug valves, explains the standard 1.5x safety factor, walks through spring-return fail-safe verification, and compares the three main pneumatic actuator types: scotch-yoke, rack-and-pinion, and spring-diaphragm.
Torque Calculations by Valve Type
Butterfly valves have the most complex torque profile because the disc is in the flow stream. The total torque has three components: seating torque (friction between disc edge and seat), dynamic torque (hydrodynamic force on the disc from flowing fluid), and bearing torque (shaft bearing friction). The formula for dynamic torque is: T_dynamic = K × ΔP × D² where K is a coefficient from the valve manufacturer (typically 0.1-0.3), ΔP is the differential pressure across the valve, and D is the disc diameter. Seating torque is typically 1.5-3x the dynamic torque at shutoff.
Ball valves have a simpler torque profile. The ball floats against the downstream seat under pressure, creating a friction torque proportional to the pressure times ball diameter times seat friction coefficient: T_ball = μ × ΔP × π × D_ball ² / 4 × D_ball / 2. Trunnion-mounted ball valves have lower operating torque because the ball is supported by trunnion bearings rather than floating against the seat, but they have higher breakout torque from packing and seal compression.
Globe valves are linear-motion valves that require thrust (force) rather than torque. The required thrust is the sum of the unbalanced pressure force on the plug (F = ΔP × A_plug) plus the packing friction force. Unbalanced globe valves have full process pressure acting on the plug area, requiring substantial thrust. Balanced plugs reduce the unbalanced area by equalizing pressure across the plug, reducing the thrust requirement by 60-80%.
Plug valves are quarter-turn valves similar to ball valves. The required torque depends on the plug taper, the sealant condition (for lubricated plug valves), and the differential pressure. Lubricated plug valves require periodic sealant injection, and seized plugs from dried sealant can require breakaway torque 3-5x the normal operating torque.
Butterfly:
T = K × ΔP × D² (K from manufacturer)Ball (floating):
T = μ × F_seat × r_ballGlobe (thrust):
F = ΔP × A_plug + F_packingAlways add 1.5x safety factor to calculated values.
Valve Actuator Sizing Check
Verify actuator torque or thrust against valve requirements. Covers butterfly, ball, globe, and plug valves with safety factor and fail-safe spring check.
The 1.5x Safety Factor and When to Use More
The standard practice is to size actuators at 1.5 times the calculated maximum torque or thrust. This 50% safety factor accounts for uncertainties in the torque calculation (valve manufacturer data is based on new, clean valves), variations in supply air pressure, increases in packing friction over time, and process conditions that may exceed the design case.
The 1.5x factor applies to the worst-case operating condition, which is usually the shutoff condition where the actuator must seat the valve against full differential pressure. For butterfly valves, the worst case may be at an intermediate position (around 70-80 degrees open) where dynamic torque peaks, not at the closed position.
Some applications require a higher safety factor. Valves in severe service (high temperature, corrosive, or erosive conditions) should use 2.0x because packing friction and seat friction increase faster than normal. Valves that sit in one position for extended periods (months or years, such as bypass valves) should use 2.0x to account for breakaway torque from static friction and corrosion bonding. ESD valves in safety instrumented systems may require additional margin per the SIL verification calculations.
Conversely, some applications can use a lower factor. Clean-service valves with PTFE packing and seats in moderate conditions may use 1.25x if the torque data is well-characterized. However, reducing the safety factor below 1.5x should be a conscious engineering decision, not a cost-saving measure. The cost difference between actuator sizes is typically 10-20%, while the cost of an undersized actuator that stalls in service is much higher.
Spring-Return Fail-Safe Verification
Spring-return actuators must close (or open) the valve on loss of air supply. The spring must provide enough torque or thrust to move the valve against the maximum process forces with zero air pressure. This is a separate calculation from the air-driven operating torque because the spring force varies with position (Hooke's law: force is proportional to compression).
For a spring-return-to-close actuator, the spring must be strong enough at its minimum compression (valve fully open) to begin closing the valve. As the valve closes and the spring compresses further, the spring force increases but the process forces may also increase (butterfly valve dynamic torque peaks at intermediate positions). The spring must exceed the process forces at every position throughout the stroke.
The spring sizing calculation starts with the maximum required fail-safe torque (including safety factor), then selects a spring set that provides at least that torque at the worst-case position. Spring cartridges come in standard sizes for each actuator, and the spring preload is adjustable (within limits) during installation. Increasing preload increases the fail-safe torque but reduces the available air-driven torque (the air must overcome the spring before it can move the valve).
The verification check is: at every valve position, the spring torque must exceed the process torque by the required safety factor. This is typically presented as a torque graph showing the spring torque curve, the process torque curve, and the safety margin between them. If the curves cross at any point, the spring is undersized for fail-safe operation at that condition. Some valve manufacturers provide software tools that generate these torque profiles automatically.
1. Spring torque exceeds process torque at all positions
2. Safety factor maintained at worst-case position
3. Air supply torque (minus spring) sufficient for normal operation
4. Spring torque at closed position does not exceed valve seat rating
5. Verify at MAXIMUM expected differential pressure, not normal
Scotch-Yoke vs Rack-and-Pinion vs Spring-Diaphragm
Scotch-yoke actuators convert linear piston motion to rotary output through a yoke mechanism. They produce a torque output that varies with position: maximum torque at 0 and 90 degrees (the "ends") and minimum at 45 degrees. This torque profile naturally matches butterfly and ball valve requirements, which have high seating/unseating torque at the closed position. Scotch-yoke actuators are the standard for large quarter-turn valves (6-inch and above) and high-pressure applications. They are available in very large sizes (up to 1,000,000 in-lbs torque).
Rack-and-pinion actuators use a linear rack engaging a pinion gear to produce rotary output. They produce constant torque throughout the stroke (unlike scotch-yoke). This makes them better for applications where the torque requirement is relatively constant across the travel range. Rack-and-pinion actuators are compact, lightweight, and cost-effective for small to medium quarter-turn valves (up to about 12 inches). They are available in both double-acting and spring-return configurations.
Spring-diaphragm actuators are the standard for linear-motion globe and cage valves. A large rubber diaphragm (12-24 inches in diameter) acts as both the pressure element and the seal. The air pressure on one side of the diaphragm pushes against a spring on the other side. These actuators are simple, reliable, and inherently fail-safe (the spring provides the failure mode). Their limitation is thrust output: they are generally limited to about 30,000 lbs of thrust, which limits the valve size and pressure class they can drive.
Selection criteria: use scotch-yoke for large quarter-turn valves, high pressures, and high cycle applications. Use rack-and-pinion for small to medium quarter-turn valves where cost and weight are important. Use spring-diaphragm for linear globe valves in standard pressure classes. For high-thrust linear applications (large high-pressure globe valves), piston-cylinder actuators with external spring returns are used.
Practical Field Sizing Tips
When replacing an actuator in the field, the simplest approach is to match the existing actuator model and size. If the existing actuator was working correctly before failure, it was sized properly (assuming process conditions have not changed). Check the actuator nameplate for the model number, size, spring range, and air supply requirement.
If the existing actuator was marginal (slow to close, stalling occasionally, or unable to seat fully), upsize by one actuator size. For scotch-yoke actuators, one size up typically provides 40-60% more torque. For spring-diaphragm actuators, one size up provides about 30-50% more thrust. This provides margin for increased packing friction and process condition changes.
When sizing a new actuator for an existing valve, get the valve torque data from the valve manufacturer. Provide them with the valve model, size, pressure class, and the maximum differential pressure across the valve. They will provide the required torque or thrust, including dynamic torque for butterfly valves. Apply the 1.5x safety factor and select the actuator from the actuator manufacturer's sizing tables.
Always verify that the actuator mounting interface is compatible with the valve. ISO 5211 standardizes the mounting flange dimensions for quarter-turn valves (F05 through F40 flange sizes). Linear valve actuators use yoke-and-stem mounting specific to each valve manufacturer. An adapter bracket may be needed for non-standard combinations. Verify the stem/shaft size, key dimensions, and height clearance before ordering.