A cam of varying throw is an adjustable cam whose effective lift can be changed during operation to alter how long an expansive valve stays open. The shifting cam carrier — usually a sliding sleeve or pivoted yoke — repositions the follower against a tapered or stepped cam profile, varying the throw without stopping the engine. This lets the operator cut off steam admission early so the remaining stroke runs on expansion alone. The result is a 15-30% reduction in steam consumption on triple-expansion marine engines and locomotives.
Cams of Varying Throw Interactive Calculator
Vary cam throw, preload, maximum throw, and admission angle to see valve cutoff, open angle, lift, and relative steam demand.
Equation Used
The cutoff fraction estimates how much of the piston stroke receives live steam. The usable cam lift is the current throw minus follower preload, divided by the usable full-throw lift, then scaled by the full-admission cam angle.
- Cam throw changes linearly along the tapered cam section.
- Follower preload is subtracted before the valve begins to open.
- Computed cutoff is limited to the practical 0 to 100 percent range.
- Relative steam demand is proportional to effective lift fraction.
How the Cams of Varying Throw (expansive Valve) Actually Works
The mechanism solves one specific problem in steam engines: you want full admission during starting and heavy load, but short admission — early cutoff — when running at speed. A fixed cam can't do both. A cam of varying throw does both by physically moving the cam profile relative to the follower, so the same shaft rotation produces different lift heights depending on cam position.
The usual layout uses a tapered cam mounted on a splined shaft. The cam slides axially along the shaft via a shifter fork driven by the engineer's reach rod. At one end of the taper the throw might be 12 mm — full admission, valve open for ~75% of the stroke. At the other end the throw drops to 3 mm, cutting steam off at ~20% of the stroke. The follower rides on whatever section of the tapered cam sits under it. The shaft itself spins at engine speed, so the timing reference stays locked while the lift amount changes smoothly.
Tolerances matter. The follower-to-cam clearance must sit at 0.05-0.10 mm at the running point. Tighter than that and the cam galls during axial shift under load. Looser and the valve hammers on opening, which you'll hear as a sharp metallic tap from the steam chest and see as pitting on the cam flank within 200 hours. The shifter fork itself needs a hardened wear pad — bronze on hardened steel cam, never steel-on-steel, because the cam rotates while the fork holds station and any galling locks the shifter solid.
Key Components
- Tapered or Stepped Cam: The working profile machined with progressively varying lift along its axis. Throw typically ranges from 3 mm (short cutoff) to 12 mm (full admission) over an axial slide of 40-60 mm. Profile is hardened to 58-62 HRC and ground to a surface finish below Ra 0.4 µm to keep follower wear acceptable.
- Splined Drive Shaft: Carries the cam at engine speed while allowing axial sliding. Splines are typically 8-tooth involute with 0.05 mm backlash maximum. Too much backlash here and the cam lags rotationally during direction reversal, which throws valve timing off by several crank degrees.
- Shifter Fork (Yoke): Engages an annular groove on the cam hub and slides the cam axially. The fork stays stationary while the cam rotates — bronze wear pads or roller bearings handle the sliding contact. Travel resolution at the operator's reach rod is typically 1 mm per notch on the quadrant.
- Roller or Flat Follower: Tracks the cam surface and transfers motion to the valve spindle. Roller followers (12-25 mm diameter) suit higher speeds above 200 RPM; flat followers tolerate the axial slide better and are cheaper to replace. Follower wear of 0.2 mm per 1000 hours is normal.
- Reach Rod and Quadrant: The operator's interface — a hand lever and notched quadrant on the footplate (locomotive) or a wheel-driven screw (marine). Each notch corresponds to a specific cutoff percentage, typically marked from 20% to 75% in 5% increments.
- Return Spring or Closing Cam: Forces the valve closed against steam pressure once the cam lift drops. Spring rate sized so the valve seats firmly within 5° of crank rotation after cam release. Underspec'd springs cause valve bounce and steam blow-by.
Who Uses the Cams of Varying Throw (expansive Valve)
You'll find varying-throw cams anywhere a working fluid needs variable admission timing under operator control. The dominant historical use was steam, but the principle migrated into early IC engines, hydraulic distributors, and a few specialised modern applications. The reason it persists is that no electronic control is needed — the operator's hand on the lever directly meters energy into the cylinder, and the linkage gives positive feedback through the reach rod.
- Marine Steam Propulsion: Triple-expansion engines on vessels like the SS Jeremiah O'Brien — varying-throw cams on the HP cylinder valve gear control cutoff from 20% to 75% to match sea state and load.
- Steam Locomotives: Stephenson and Walschaerts valve gear variants on locomotives such as the LNER A4 Pacifics used shifting expansion links functionally equivalent to varying-throw cams, giving drivers cutoff control from 15% to 75%.
- Stationary Steam Engines: Corliss-type engines built by Hick Hargreaves and similar firms used varying-throw release cams to govern cutoff against load — the cam throw shifted automatically via the flyball governor.
- Early Internal Combustion: Pre-1920 stationary gas engines like the Otto Atmospheric used cam-shifted intake timing to govern speed without throttling — load-sensitive cam shift held a constant RPM.
- Hydraulic Distribution Valves: Heavy-press hydraulic systems on forging machines like Schuler eccentric presses use varying-throw cams to vary stroke-end dwell and fluid admission timing during long-stroke operations.
- Industrial Air Compressors: Older Ingersoll-Rand reciprocating compressors used variable-throw unloader cams to reduce capacity at light demand instead of cycling the motor.
The Formula Behind the Cams of Varying Throw (expansive Valve)
The single most useful calculation is cutoff fraction — what percentage of the piston stroke the valve stays open. This determines how much steam enters and therefore how much expansion does the work. At the low end of typical operation (15-20% cutoff) the engine runs efficient but weak — fine for cruising a fully-loaded locomotive on level track, useless for starting. At the high end (70-75% cutoff) you get maximum torque but burn coal at twice the rate. The sweet spot for most marine triple-expansion engines sits at 35-45% cutoff at cruise, which is exactly the cam-throw range the gear is designed to favour.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Coff | Cutoff fraction — proportion of stroke during which valve stays open | dimensionless (0 to 1) | dimensionless (0 to 1) |
| hcam | Current cam throw at operator's lever position | mm | in |
| hpreload | Follower preload offset before valve cracks open | mm | in |
| hmax | Maximum cam throw at full-admission lever position | mm | in |
| θadmission | Crank angle over which cam lobe acts at full throw | degrees | degrees |
Worked Example: Cams of Varying Throw (expansive Valve) in a vintage Corliss stationary engine restoration
You are restoring a 150 HP Corliss stationary engine driving a sawmill line shaft. The HP cylinder uses a varying-throw release cam with a maximum throw of 14 mm, follower preload of 2 mm, and an admission lobe acting over 180° of crank rotation. You need to know what cutoff percentage you get at three lever settings: short (hcam = 4 mm), nominal cruise (hcam = 8 mm), and full admission (hcam = 14 mm).
Given
- hmax = 14 mm
- hpreload = 2 mm
- θadmission = 180 degrees
- hcam,low = 4 mm
- hcam,nom = 8 mm
- hcam,high = 14 mm
Solution
Step 1 — at nominal cruise lever (hcam = 8 mm), compute effective throw above preload:
Step 2 — divide by maximum effective throw and multiply by the admission arc fraction:
That's a respectable cruise cutoff — the steam admits for 25% of stroke, then expands through the remaining 75%. The engine pulls a steady mill load at this setting and burns coal at a sensible rate.
Step 3 — at the short-cutoff end of the lever (hcam = 4 mm):
This is too short for most loads. The engine wheezes — torque drops to roughly a third of nominal and the flywheel will stall under any sudden cut, like a fresh log hitting the saw. Useful only for light idle running.
Step 4 — at full admission (hcam = 14 mm):
50% cutoff is full-grunt territory. You'd use this only for starting from rest under load or cresting a heavy demand spike. Steam consumption roughly doubles versus 25% cutoff for maybe 60% more torque — which is why an engineer who leaves the lever here ends up burning twice the coal his neighbour does.
Result
At nominal lever position the cutoff is 25%, meaning steam admits for the first quarter of stroke and expands through the rest. The engine sounds smooth, the exhaust beats are crisp, and steam pressure holds steady. At the short-cutoff end (8.3%) the engine becomes anaemic and stalls under load swings; at full admission (50%) torque jumps but coal burn doubles. If your measured cutoff differs from predicted by more than 3-4 percentage points, suspect: (1) worn shifter fork wear pads letting the cam drift axially under follower side-load — check the bronze pad thickness against the original 6 mm spec, (2) splined shaft backlash exceeding 0.1 mm causing rotational lag during reversing, or (3) follower preload spring sag, which raises hpreload by 0.5-1 mm and shortens cutoff measurably without any visible cam wear.
Cams of Varying Throw (expansive Valve) vs Alternatives
Varying-throw cams are one of three classical ways to get variable valve timing. Picking between them comes down to mechanical complexity versus what you're willing to spend on machining and how fast the engine runs.
| Property | Cam of Varying Throw | Stephenson Link Motion | Cam-Shifting (Multi-Lobe) Cam |
|---|---|---|---|
| Operating speed range | 50-400 RPM | 30-500 RPM (locomotives to 600 RPM peak) | 1000-8000 RPM (modern IC engines) |
| Cutoff resolution | Continuous, ~1% per lever notch | Continuous via reverser screw | Discrete steps (typically 2-3 lobes) |
| Manufacturing complexity | High — tapered ground cam, splined shaft | Medium — link, dies, eccentric rods | Very high — multi-lobe ground cam plus hydraulic shifter |
| Service life under steam | 8000-15000 hours before regrind | 20000+ hours, simpler wear pattern | Not used in steam |
| Operator response time | Direct mechanical, <1 s lever to valve | Direct mechanical, <1 s | Electronic, ~50-200 ms |
| Best application | Stationary and marine engines needing fine cutoff trim | Locomotives needing reversing plus cutoff | Modern IC engines (VVT systems like Honda VTEC) |
| Relative cost (period dollars) | Medium-high | Medium | High (modern hydraulic actuation) |
Frequently Asked Questions About Cams of Varying Throw (expansive Valve)
Almost always the new cam has a slightly different preload offset than the original. If the regrind shop took 0.5 mm off the base circle to clean it up, your hpreload dropped — but they likely shimmed the follower back to zero clearance, which doesn't restore the original geometry. The cam now opens the valve a few crank degrees earlier and closes it a few degrees later, but with reduced peak lift.
The fix is to measure the original base-circle radius from a drawing or surviving twin engine and shim the cam-shaft mounting block, not the follower. Shimming the follower changes the geometry of the rocker arm and shifts the angular timing of admission — which is why power goes down even though the lift seems right.
Tapered cams give continuous adjustment — you can sit at 23.7% cutoff if you want — but they wear unevenly because the follower sits on a different cam strip every operating point. After 5000 hours you'll see distinct wear bands and the cam needs regrinding across its full width.
Stepped cams give you 3-5 fixed cutoff positions, wear evenly within each step, and are easier to manufacture. Pick stepped if your application has a few well-defined operating modes (start / cruise / high-load) and tapered if the operator needs to trim continuously against varying conditions, like a marine engine in a head sea. Most stationary engines do better with stepped because operators don't actually trim continuously — they pick a setting and leave it.
The lever-to-cam linkage has lost motion. There are three places it hides: the reach rod end pins (look for elongated holes), the shifter fork sliding clearance against the cam hub groove, and the splined shaft's rotational backlash. Add them up and you can easily see 5-7% cutoff error.
Diagnostic check: with the engine stopped, push the lever firmly to the full-admission stop and mark its position on the quadrant. Then pull it back with steady force to the short-cutoff stop and mark again. Now cycle the lever rapidly between the marks and watch the cam — if the cam doesn't move the full distance, you've found your slop. Replace pins first, fork pads second, splined shaft last (most expensive).
Yes, but the economics rarely work unless the engine runs at varying loads. A fixed-cam engine running at constant load doesn't benefit — the original cam was sized for that operating point and any variable system just adds linkage and wear without saving steam.
The retrofit pays off when load varies by 30% or more during a duty cycle. Marine auxiliaries that go from idle (running an alternator) to full pump load are good candidates. The cost of the splined shaft, tapered cam, shifter, and reach rod typically equals 6-18 months of saved coal — beyond that you're ahead. Below that load variability, leave the fixed cam alone.
Short cutoff means the valve closes early and the trapped steam expands deeply — pressure in the cylinder drops well below boiler pressure before exhaust opens. If your exhaust valve timing is fixed (only admission is variable), the pressure differential at exhaust opening becomes large and you get a sharp pressure spike or vacuum collapse that sounds like a knock.
Two fixes: either accept that short cutoff isn't useful below a certain load and stop using it, or fit a variable exhaust release cam alongside the admission cam — Corliss engines did this with four separate cams (two admission, two exhaust) so all four events could be tuned. The knock is a timing mismatch, not a mechanical failure, so don't go looking for loose bearings until you've checked it disappears at longer cutoff.
The cam shaft, cam, and shifter fork sit in or near the steam chest at 180-220°C in a typical engine. Carbon steel expands roughly 12 µm/m/°C, so a 60 mm cam-axial-travel range can grow by 0.13-0.16 mm between cold start and full operating temperature. That's small but enough to shift cutoff by 1-2% — which an attentive engineer notices as the engine seeming to settle into its rhythm 10-15 minutes after firing.
If you want consistent timing, mount the shifter fork in a bracket that grows with the cam shaft (same material, same temperature) rather than off the cold engine frame. This is why old Corliss engines mounted the valve-gear quadrant on a stub off the steam-chest casting, not the bedplate — they wanted the geometry to track temperature.
References & Further Reading
- Wikipedia contributors. Cutoff (steam engine). Wikipedia
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