Valve stroke time — how fast a control valve moves from one position to another — is critical for process safety and control performance. Emergency shutdown valves must close within a specified time (often 2-5 seconds) to protect equipment and personnel. Control valves must respond fast enough to keep up with process dynamics but not so fast that they cause water hammer or pressure surges.
Stroke time depends on three factors: the volume of the actuator, the flow capacity of the air supply path (tubing, solenoid valves, positioner), and the supply pressure available to drive the air into or out of the actuator. If any one of these creates a bottleneck, the stroke time increases. The most common cause of slow valves is undersized tubing or a restricted solenoid valve that cannot deliver air fast enough to fill the actuator.
This guide covers the fundamentals of stroke time calculation, explains the series Cv concept for analyzing the air supply path, and discusses when volume boosters or quick exhaust valves are needed to meet stroke time requirements.
Calculating Actuator Volume
The first step in stroke time calculation is determining the actuator volume that must be filled with air to move the valve. For diaphragm actuators, the volume is the effective diaphragm area times the stroke: V = A_eff × stroke. The effective area is not the full diaphragm area because diaphragm geometry causes the effective area to decrease as the stroke increases (rolling diaphragm effect). Manufacturers publish the effective area or total volume in their data sheets.
For piston actuators (scotch-yoke and rack-and-pinion), the volume is the cylinder bore area times the piston travel: V = π × D² / 4 × stroke. Scotch-yoke actuators for quarter-turn valves typically have piston travels of 4-12 inches depending on size. Double-acting piston actuators require air on both sides, so the total volume that must be moved during a stroke is the cap-end volume plus the rod-end volume.
For spring-return actuators, the fill stroke (against the spring) requires delivering air at supply pressure to overcome both the spring force and the process forces. The exhaust stroke (with the spring) requires exhausting the air to atmosphere while the spring provides the driving force. The fill stroke is almost always slower than the exhaust stroke because the supply path has more restrictions (solenoid, positioner, tubing) than the exhaust path.
Common actuator volumes: a Fisher 1061 size 40 actuator is approximately 180 cubic inches. A size 60 is about 450 cubic inches. A size 70 is about 700 cubic inches. A Valvtechnologies 4-inch high-performance butterfly with a scotch-yoke actuator might be 300 cubic inches. These volumes determine how much air must flow through the supply path during each stroke.
Diaphragm:
V = A_effective × stroke (get A_eff from datasheet)Piston:
V = π × D² / 4 × piston_travelAir required (SCF):
V × (P_supply + 14.7) / (14.7 × 1728) Valve Stroke Time Calculator
Calculate pneumatic valve stroke time from actuator volume, supply pressure, and system Cv. Identifies undersized tubing and slow-stroking valves.
Series Cv: The Bottleneck Concept
The air supply path from the header to the actuator contains multiple restrictions in series: the filter-regulator, the solenoid valve (if used), the positioner (if used), the tubing, and any fittings. Each restriction has a Cv that limits flow. The combined Cv of restrictions in series is always less than the smallest individual Cv.
The series Cv formula is: 1/Cv_total² = 1/Cv_1² + 1/Cv_2² + 1/Cv_3² + ... This is analogous to resistors in parallel in electrical circuits. If a solenoid has Cv = 1.5 and the tubing has Cv = 4.0: 1/Cv_total² = 1/1.5² + 1/4.0² = 0.444 + 0.0625 = 0.507. Cv_total = √(1/0.507) = 1.40. The solenoid is the bottleneck — it limits the total path Cv to 1.40, barely less than the solenoid alone.
This is why a small solenoid valve can dominate stroke time even with large tubing. A typical 1/4-inch NPT solenoid has a Cv of 0.9-1.5. A 3/8-inch solenoid has Cv of 2.5-4.0. Replacing a 1/4-inch solenoid with a 3/8-inch solenoid can reduce stroke time by 50% or more on large actuators where the solenoid is the dominant restriction.
Tubing Cv depends on the inside diameter, length, and number of fittings. Short runs of 3/8-inch tubing have Cv values of 3-5. Long runs (over 50 feet) or runs with many fittings have lower effective Cv. The tubing Cv can be estimated from the Harris formula pressure drop: Cv_tube = Q × √(G_g × T / (ΔP × (P1 + P2))) at the expected flow rate.
1/Cv_total² = 1/Cv_1² + 1/Cv_2² + 1/Cv_3²The total is always less than the smallest individual Cv.
Identify and upsize the component with the lowest Cv to improve stroke time.
Fill Time and Exhaust Time Formulas
Fill time (the time to pressurize the actuator from atmospheric to supply pressure) can be approximated by: t_fill = V / (Cv_path × 22.7 × √(ΔP_avg × P_avg / T)) where V is the actuator volume in cubic inches, Cv_path is the total series Cv of the supply path, ΔP_avg is the average pressure drop during fill, and P_avg is the average absolute pressure during fill. This simplified formula assumes isothermal conditions and provides a reasonable estimate for engineering purposes.
A more practical approach for field estimates is the charging time constant method. The time constant τ is proportional to the actuator volume divided by the supply path flow capacity. Fill time to 63% of final pressure is one time constant. Fill time to 95% is three time constants. Fill time to 99% is five time constants. For a spring-return actuator, the valve begins moving as soon as the air pressure overcomes the spring preload, so the actual stroke begins before the actuator is fully pressurized.
Exhaust time is typically 80-85% of fill time for the same path Cv, because the exhaust path is usually less restricted (no solenoid in the flow path, positioner exhaust port is larger than inlet). However, if the solenoid is in the exhaust path (common in trip valve circuits), exhaust time may equal or exceed fill time. Some solenoid valves have different Cv values for forward flow versus exhaust flow.
For emergency shutdown (ESD) valves, the critical requirement is usually the exhaust stroke time (fail-closed valves exhausting to close). API 6D and plant safety studies specify maximum stroke times. If the natural exhaust time exceeds the requirement, quick exhaust valves or volume boosters are installed to bypass the solenoid and provide a high-Cv exhaust path directly to atmosphere.
Volume Boosters and Quick Exhaust Valves
When the natural stroke time exceeds the requirement, the solution is to increase the Cv of the air supply path. The three options are: upsize the tubing, upsize the solenoid, or install a volume booster. Volume boosters are pneumatic amplifiers that take a small pilot signal and deliver a large volume of air from a local supply. They are installed near the actuator and piped to a local air supply header.
A volume booster has a small pilot port (1/4-inch, low flow) connected to the I/P or positioner output, and a large output port (1/2-inch or 3/4-inch, high flow) connected to the actuator. When the pilot pressure changes, the booster replicates the pressure change on the output with much higher flow capacity. A typical booster has an output Cv of 5-15, compared to a positioner output Cv of 0.5-2.0.
Quick exhaust valves are simpler devices that provide a direct path from the actuator to atmosphere. They are installed at the actuator port and open when the supply pressure drops (during a trip). The actuator air exhausts directly through the quick exhaust valve instead of traveling back through the tubing and solenoid. This is the standard solution for ESD valves where fast closure is the critical requirement and precise control of the opening stroke is less important.
Boosters introduce control challenges. Because they amplify both the signal and any noise, they can cause valve oscillation if not properly adjusted. Most boosters have a deadband adjustment (bypass) that allows small signal changes to pass through without triggering the booster. Setting the deadband too narrow causes hunting; setting it too wide defeats the purpose of the booster. Typical deadband settings are 1-3 PSI.
1. Stroke time exceeds requirement by more than 50%
2. Upsizing tubing and solenoid alone is insufficient
3. Actuator volume exceeds 300 cubic inches with standard positioner
4. ESD valve requires fail time under 3 seconds
When NOT to use a booster: tight throttling control applications where the booster deadband causes hunting.
Diagnosing Slow Valve Response in the Field
A valve that strokes slower than expected has a restriction somewhere in the air supply path. The systematic diagnosis approach is to measure pressure at multiple points while stroking the valve and look for excessive pressure drops.
Step 1: Measure supply pressure at the filter-regulator output while stroking the valve. If the pressure drops more than 2 PSI during the stroke, the filter-regulator is undersized or the filter element is plugged. Step 2: Measure pressure at the solenoid output while stroking. A drop of more than 5 PSI across the solenoid indicates the solenoid is the bottleneck. Step 3: Measure pressure at the actuator port while stroking. A large difference between the solenoid output and the actuator port indicates a tubing restriction (undersized, kinked, or plugged tubing).
Common causes of slow stroking that are not obvious: kinked tubing behind cable trays or inside conduit boxes, corrosion buildup in old black iron supply lines, solenoid valves with the wrong orifice size (spare installed with smaller orifice than original), positioner output ports partially blocked with pipe tape or thread sealant, and quick disconnect fittings with reduced internal bore.
After any repair, measure the actual stroke time with a stopwatch and record it. The measured time becomes the baseline for future comparison. Most plants record stroke times during annual partial stroke tests for ESD valves. A progressive increase in stroke time over multiple tests indicates a developing restriction that should be investigated before it causes a test failure.