Shay Power & Tractive Force
Nelson Riedel
Initial: 05/22/06 Last Revised: 12/03/2008

The first time I had the shay on the track with other larger steamers and diesels I felt a bit inferior because they had more power and ran faster.   This was most pronounced if some of the other locomotives were 2.5" scale narrow gauge running on the 7.5" gauge track.  

This spring and my son Andy and I visited Jim Zealer's track in nearby Pataskala, Ohio.  The main purpose of the trip was to observe a large narrow gauge Mikado.  I took the shay along hoping to get a chance to try it out on the steep grades Jim had told me would be an ideal test for a shay.  Jim lent me about eight cars.  Andy, Dick McCloy and his dad Sid and I boarded and away we went.    Within 100 yards the shay was struggling and several times I had to stop to build steam.  One time I built the steam to 120 psi and opened the throttle and the wheels actually slipped.  It was like I was dragging an anchor.  And yes, the parking brake was off.  The final test was the steep slope on the final loop.  I took it really slow, maybe 5 scale mph (on the bicycle speedometer) but stalled when the pressure dropped to 80 psi.   Stopped, build a little steam and finally made it over the hump and  back to the yard before that Mikado ran over us.

We took a break and tried to figure out what was wrong.  Dick suggested maybe the load was too great ---- maybe we all had been consuming too many pizzas.  The eight cars were pretty heavy, maybe 200 lbs each. The shay is maybe 500 lbs and the four people weigh about 800 lbs so that's 3000 lbs total.  The grade seemed really steep, maybe 6%.  That means the force required to move the train up that grade was about 180 lbs.  Some time back I'd used an on-line calculator to compute the shay tractive force as part of the design process for the engine on the Heisler project.  I recalled that calculator indicated that the maximum tractive force for the shay at 100 psi was ~ 200 lbs, so maybe  I should have expected it to stall --- maybe I was trying to pull too much.   Later, I cut off half the cars and half the people and was able to climb all the grades with no difficulty.  I was also able to maintain steam pressure if I went really slow. 

There are two issues here:

  • What load can the shay pull --- this is a tractive force issue.

  • At what speed can the shay pull the load while maintaining pressure --- this is a power issue.       

Relating the steam pressure to the starting tractive force is a simple high school physics problem .  I should be able to measure this force using an inexpensive scale of sorts.  The power issue is  more complex so I decided to deal with the force issue first.

Tractive Force:

The graph above shows how the starting tractive force changes as a function of the crank position.  There are three double acting pistons and each piston has a peak torque point each half crankshaft cycle and the peaks are evenly distributed around the crankshaft rotation so the three peaks on the graph should be expected.  The sharp drops are less obvious. A valve closes to admission at 85% of the stroke (85% cutoff) which corresponds to 135 degree crank rotation from the start of the stoke.  The valve opens to exhaust a bit further on in the rotation.  From a starting traction point of view, a piston with a closed input or open exhaust valve generates no force.  The sharp drops correspond to the points where a valve closes to admission.  Note that the normalized values range from a minimum of 1.2 to a maximum of 1.9. 

The complete equation for the shay starting tractive force is:

Tractive Force (min) =  1.2 X (Boiler Pressure) X ( Piston Area) X (Stroke) x (Gear Ratio) / (Wheel Diameter)          

Tractive Force (max) =  1.9 X (Boiler Pressure) X ( Piston Area) X (Stroke) x (Gear Ratio) / (Wheel Diameter) 

For my shay,

  1. the the working boiler pressure is 100 psi

  2. the piston diameter is 1.375" giving an area of 1.48 sq in.

  3. The stroke is 1.5"

  4. The gear ratio is 2

  5. The wheel diameter is 4"

These values compute to 133 lbs min and 210 lbs max starting tractive force.

The next step was to measure the force.  The first attempt was to push against a large bathroom scale.  The readings were in the ballpark but unstable because we were unable to hold the scale perpendicular to the track. I had no confidence in the data.

The next step was to purchase a linear hanging spring scale with a 330 lb capacity from McMaster-Carr (#1756T5). One end of the scale was connected to the coupler with a ~ 6 ft cloth strap and the other end was wrapped around  a track stop.  The end at the stop was held by an able assistant. The assistant could release a small amount of strap and then hold that position so readings could be taken at various crank positions.

The photo above shows taking a measurement while backing.  That is Dick McCloy managing the strap.

 Photo above shows one of the scale readings --- in this case one of the highest readings while backing.  The readings ranged from 125 lbs to 185 lbs while backing and 125 lbs to 175 lbs while going forward. Interestingly, the engine didn't slip while going backward (with no engineer) but did slip at some crank positions when heading forward.  The slipping stopped when the engineer got on board. (Maybe oil dripped on the track between the two tests.)  These measurements were taken at ~ 110 psi steam pressure.  The readings at 100 psi should be ~ 9% less or  115 lbs to 170 psi.    Recall that the computed range was 133 to 210 lbs.

At first glance, the measurements are well below those computed and were disappointing.   The first thought was that the pressure on the pistons was less because of valve and packing leaks.  However, there weren't noticeably large leaks and since the pistons were not moving and the throttle was wide open, the pressure might be the most stable part of the setup.

Next, I closed the throttle and measured the force to get the locomotive moving --- about 25 lbs --- this is friction.  The measured 115 lbs to 170 psi was after the friction loss.  If the 25 lbs friction loss is added back in, the force generated by the engine is 140 lbs to 195 lbs, very close to that calculated..  

(Later in the day Dick and Dan Staron measured the the tractive force on Dan's shay and got slightly lower readings but Dan was at 100 psi so they were probably consistent the measurements on my shay.)

Next, we used the scale to measure the tractive force of a couple of Dick's diesels.  The photo above shows Dick on his SW1500.  This locomotive generated ~225 lbs force and then started slipping.   We also tested his FA and found it slipped at about 250 lbs. 

The tractive force determines how much of a load the locomotive can get moving.  The measurements tell us that the diesels can get about twice the load moving as the shay.

Next question is --- how much load can the Shay move around  Dick's Mill Creek Central Track?   The track has a maximum  grade of  ~3.5%.  I can probably maintain 100 psi at the short distance that is the maximum grade so how many cars can I pull?  I used the scale to pull a dozen hopper cars in the level yard and found it took less than 10 lbs.  So, it's probably sufficient to deduct the 25 lbs for the locomotive friction and forget the car friction.  The question then is what weight train will require generate a 115 lb tractive load on a 3.5 % grade?   If we divide 115 lbs by 0.035, we find the max train weight is 3285 lbs.  the locomotive and engineer together weigh ~ 700 lbs so the rest of the train can weigh 2600 lbs.  If the cars weigh 200 lbs each, then a maximum of 13 cars can be pulled around the track.

The above photo shows the shay pulling 15 cars and we made it all around the track with no problem as far as the tractive effort (the speed is another issue).  So, is my calculation wrong? Yes, the cars probably weigh less than 200 lbs each and the engineer shown in the photo is pretty skinny so the locomotive plus engineer probably weighs less than the 700 lbs estimate.   


The previous measurements show that the shay produces about half the usable tractive force as Dick's diesels.  However, the shay probably produces about one tenth the power. For example, I could maintain pressure at a speed of about 6 scale mph on the lesser slope parts of the track with the 15 car load pictured above.  Dick's diesels would have no trouble pulling the same load at 60 scale mph or faster. 

The capability to produce steam is the limiting factor with the shay.  The ability to produce steam is limited by the firebox size.  (Ken Schroeder pointed out that there was room to extend the firebox a few inches on the three truck configuration.  I should have followed up on that observation before ordering the boiler.)  There is a clear speed-load trade off. If you run too fast with a given load, the pressure will drop and you have to slow down or stop to build pressure before tackling a long grade.

There is very little energy storage in the small shay boiler so one must limit the speed to match the steam generation capability. However, one can get the most use of the the small storage but managing the water level.  One can add water on the downgrades and flats and get to maximum pressure at maximum water before tackling the more difficult grades and then stop adding water on the grade.  

A nagging question ---- how many HP is the Shay ---- or more accurately --- how may HP can the boiler/firebox produce.  The ideal way to measure this is to have a setup where the shay is pulling a constant load and the throttle is adjusted so that pressure is maintained while just enough water is added to replace that consumed.   That sounds like a difficult setup.

However, as a rough guess, I think I can pull about half the minimum starting tractive force at about 10 scale mph. I have a bicycle speedometer setup for scale mph.  I set this speedometer up for 1.6" scale so the 10 mph is 1.33 actual mph which is 7022 ft/hr or 1.95 ft/sec.  If I can generate 70 lbs tractive force at this speed and maintain pressure, the power is 137 ft-lb/sec.  Recall that one HP is 550 ft-lb/sec, so the 137 ft-lb/sec is about 0.25 HP. How accurate is this?   I don't know.  But I'm sure that it not off by more than a factor of 4 so the  power is definitely between 0.1 and 1 HP.  Next time at the track I'll have to try to get a better handle on this.

Another way to try to get a handle on the power is to measure the fuel usage and convert that to BTU and then try to guess at the system efficiency.  Maybe I can work that out to within a factor of 2.

Update 12/03/2008

This past summer I got an email from John Pickering in the UK.  John has been doing some research in anticipation of building a Shay.  Part of his input is as follows: 

 I have some comments on the web page on power and tractive force. If you go to you can download a spreadsheet called "engine" which predicts locomotive performance. I have not yet bought Kenneth Schroeder's drawings but suspect that his boiler is similar to The Hiraoka design, albeit with more fire tubes. If I enter the parameters I know for Kenneth Schroeder's design with the Hiraoka boiler, but with 25 half inch tubes, it predicts a tractive effort of 180.8 lbs at 85% of normal boiler pressure. More important it estimates the boiler performance. The spreadsheet is intended for coal fired loco's, if we assume it is fired with 1" coals and has a 2" fire bed it predicts 17.69 KW. to the steam at a boiler efficiency of 66.35%. This corresponds to a thermal input of 26.66 KW. At the IMLEC. model efficiency trials the best models achieve over 1% thermal efficiency but most are a little under this value. If we assume your Shay achieves around 1%, the sustained mechanical output would be 267 W. or 0.358 BHP. Quite close to your measured values. As you say it is the ability of the boiler to produce steam which is the limiting factor. If my 60 ton class C ever sees the light of day may be it will get the longer firebox!

I just completed some more modifications to the smoke box and fire box described at More Power so the thought of measuring the total output power is on my mind again.    It's winter now and too cold for tests --- but I have some time to plan for tests in the spring.  I plan to review some of the articles on the model engineering website Jon Pickering mentioned above ( .  Another reference point is the amount of heat generated by the oil fire.    The heat content of the diesel fuel is 146,000 BTU/Gal.   At 3413 BTU per KWH this converts to 42.7 KWH/gal fuel.  At 1% efficiency this corresponds to 427 WH/gal of fuel consumed.   My guess is that I'm consuming about a gallon or slightly more fuel per hour at full burner setting.  (That's something to measure next year.)  If the consumption is exactly 1 gal/hr and the efficiency is exactly 1%, then the power output is 427/745 = 0.57 HP.  

End 12/03/2008 Update

More Tests

After taking all the measurements Dan Staron and I hooked our shays together and hauled a string of 27 cars (if I counted correctly) around the track.  The total track length is about a mile and with this load each trip took about 45 minutes.  One might ask, what is the probability of two steam locomotives running for 45 minutes without a problem? We did get a couple loops without a breakdown.  However,  I had a problem all day getting enough water to the boiler.  After checking the pump and scratching my head, Dick McCloy suggested the strainer screen might be partially plugged.  Good idea!  Later, a screw came out of the bracket securing Dan's axel pump.  Then my tubes became so sooted that I couldn't make it back without cleaning them. (I had not cleaned the tubes this year in a test to see how long I could go.  The new fire pan has worked out great.  If I clean the tubes once each day and adjust the blower and fuel levels so there is no smoke, it works great!)

The following photo show Dan and I playing engineer:

We've just left the upper yard and sped down the long hill (above).

On to the long flat stretch (above).

Starting up the long hill to the reverse loop (above).

At the 3.5% grade near the top of the reverse loop hill (above).

Coming off the hill past the lower yard and heading to the tunnel (above).

 Over the creek and through the woods.....(above).

The grade crossing (above).

Building steam for the long hill to the upper yard  (above).

       We made it back to the yard with no breakdown this time!

It was a beautiful spring day!  Many thanks to Dick McCloy for sharing his track and taking the photos.  For more information on Dick's Mill Creek Central track see


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