Amperage to Tractive Effort table for an SD40-2

Several people have asked me if I have an Amps to Tractive Effort chart. The answer is no. I don't think it is possible to use one chart to convert amps to tractive effort for several reasons.

1. The amps depend upon the gearing of the locomotive. The higher geared the higher the amps at any given speed. Yet the tractive effort is solely a factor of horsepower and speed. So two locomotives with the same horsepower that have different gear ratios would produce different amps at any specified speed but the TE would be the same.

(Note: At any given loco speed a higher geared loco's TMs will be rotating slower than a lower geared loco's. This results in higher TM amps on the higher geared loco. This higher amperage results in a higher torque at the TM shaft. But the higher gearing between the motor shaft and the wheel decreases that torque at the wheel right back down to the same value as the lower geared loco. Thus the TE of the two locos for any given speed is equal regardless of gearing and the laws of physics are preserved.)

2. The amps depends upon traction motor design and the applied voltage. Different builders use different designs and different operating voltages so the traction motor amperage of different builders are going to differ even if the locos are equal horsepower.

3. The amps of a locomotive depends upon the number of traction motors. Two 3,000 Hp locos, say a 4 axle GP40 and a 6 axle SD40, are going to have widely differing traction motor amperages simply because the total Hp is spread over different numbers of motors. A GP40 will produce 50% more amperage at any given speed than an SD40 will yet the tractive effort of both will be identical.

Problem number 3 above can be circumvented by creating a chart of TE PER TRACTION MOTOR vs Amperage rather than a Loco TE vs Amperage chart.

That leaves problems number one and number two above. So the best we can do is create a different chart for each builder and each gear ratio. In fact it will probably have to be a separate chart for each TM model even if they are from the same builder. Thus a single general amps to TE chart won't work.

A chart of this type is presented below. It is made from direct observation of the ammeter on Burlington Northern 7200 series SD40-2s. The Tractive Effort column is the theoretical tractive effort of a 3,000 Hp loco for each speed. Locos are rated at "Horsepower for traction" which basically means the Hp of the diesel engine after the Hp for accessories such as pumps and fans has been subtracted. It is the Hp put into the main generator. But the generator (alternator), wiring, traction motors, and gearing are not 100% efficient. There is some power loss in each of them. I feel an efficiency of about 85% is a good number to use based on decades of field experience making calculations of Hp, tonnage, grade, and speeds while running actual trains. Thus I have included an 85% efficiency column in the chart which gives a close approximation of the actual tractive effort obtained. The Multiplier column is the multiplier needed to be applied to the amps to get the 85% traction effort figure. You can see this is not a single number. Since this chart is for but a single class of a single model and the multipliers are not a constant you can see that a single conversion constant for amperage to tractive effort for all models is not possible.

*The two lowest speed values, 7 mph & 10 mph, may bit a bit high on the estimated TE account I assume the loco is putting out its full rated 3,000 Hp. But in reality the output is probably reduced a bit account of wheelslip control at those speeds.

My Tractive Effort vs EMD'sNote that a graph could be made from the above chart showing the tractive effort produced for any amperage for that locomotive class. I have such a graph from EMD showing the Tractive Effort per Traction Motor verses Amperage. The graph is for 62:15 gearing and D77 motors under full field operation. My figures for the chart above are taken from ammeter readings on actual SD40-2s. The chart below compares EMD's projections, which I have taken from their graph, to my actual readings and calculations in the above chart. Looking at the chart below you can see the two values compare favorably. Again, the 1200 amp and 1050 amp figures are a bit off because in my chart I assumed full 3,000 Hp operation but in reality at those low speeds the wheelslip control module has probably reduced diesel engine output to control wheelslip. The difference is reflected in the discrepancies between EMD's figures and mine at the slowest speeds (highest amperages). Another factor explaining this discrepancy may be that the TMs are not as efficient at the extreme lower rpms.

My Tractive Effort vs EMD's

Note that a graph could be made from the above chart showing the tractive effort produced for any amperage for that locomotive class. I have such a graph from EMD showing the Tractive Effort per Traction Motor verses Amperage. The graph is for 62:15 gearing and D77 motors under full field operation. My figures for the chart above are taken from ammeter readings on actual SD40-2s. The chart below compares EMD's projections, which I have taken from their graph, to my actual readings and calculations in the above chart. Looking at the chart below you can see the two values compare favorably. Again, the 1200 amp and 1050 amp figures are a bit off because in my chart I assumed full 3,000 Hp operation but in reality at those low speeds the wheelslip control module has probably reduced diesel engine output to control wheelslip. The difference is reflected in the discrepancies between EMD's figures and mine at the slowest speeds (highest amperages). Another factor explaining this discrepancy may be that the TMs are not as efficient at the extreme lower rpms.

Dynamic Braking Force vs Locomotive Speed

Similarly people have asked me for an amperage to dynamic brake force chart. For much the same reasons that you cannot have a single Amps to TE chart you also cannot have a single Amps to DB Force chart.An SD40-2 in full dynamic braking produces approximately 700 amps DB at all speeds above about 25 mph. Yet when running trains it is very obvious that that 700 amps of DB current produces much more retardation force at the lower end of this speed range than at the higher end. In other words 4 SD40-2s, each producing 700 amps of DB, will hold (or even slow) a 6000 ton train on a 1.2% grade at 30 mph but will not hold the same train on the same grade at 50 mph. It will run away, continuing to accelerate. So the amps alone is not enough to determine the DB force.

The best you can do is state that each axle of DB can produce a maximum of 10,000 to 15,000 lbs of retardation force. The maximum force varies with the era the loco was built and is roughly related to the locomotive's traction horsepower. The higher the loco Hp generally the higher the maximum DB force.

As an example: A 3,000 Hp SD40-2 may produce a maximum of 10,000 lbs of DB force for each axle or 60,000 lbs total. A 4,000 Hp SD70MAC of 20 years later produces 86,000 lbs maximum DB force. Keep in mind the DB force produced is directly related to the number of axles a loco has. Thus a 6 axle 6 motor unit will produce 50% more DB force than a 4 axle 4 motor unit of the same Hp from the same era.

Below is a Speed to DB force chart. You can see how the DB retardation force drops off with increasing speed above 25 mph even though the DB current remains constant at 700 amps.