No more excuses for out of whack train acceleration physics lol

Video Transcript:

So in the game of OpenBVE, there has been a bit of uncertainty about what is the

proper and accurate acceleration curve for NYC subway rolling stock. Sometimes the

trains are programmed too slow, sometimes they are too fast. Well, no more. Here

and now, I will show you exactly how to calculate a particular train's maximum

acceleration curve JUST by knowing what the rated power (kW) and weight (m) values

are.

Eventually, I will run through all of the Post-Unification stock and nail down their

individual max acceleration curves, but for the sake of this demonstration, I will

only focus on 4 trains (R1, R32, R142A, R160), one from each generation of stock (plus

an IRT NTT train).

Above, I did state that you only need weight and power rating to calculate the max

acceleration curve, but really, those are the constant variables. If you are to do

the calculations, you need to also know the changing variable, which is either

rated acceleration, or rated tractive effort. Since we know that the maximum starting

acceleration of an NYC subway car is 2.5 mph/s (4.0225 km/h/s) for all stock R10 and

newer, and 1.75 mph/s (2.81575 km/h/s) for R1-R9 stock, all our variables are accounted

for. So let's begin with the R32.

For the sake of clarity, I will try to show both

metric and imperial measurements. I will include a conversion table here:

Weight:

1 Kilogram = 2.2046 lbs

Power:

1 Kilowatt = 1.34 hp

Speed:

1 mph = 1.609 km/h

Acceleration:

1 ms^2 = 3.6 km/h/s = 2.237 mph/s

For each of the calculations, I will be using the values from a single car (not a

full train set) since each car is motorized; acceleration curves will be constant.

This is not the case for the R142, R142A, and R188, which do have unpowered trailer

trucks that must be accounted for. Those values will have to be calculated by train.

Now that we have those values for the R32 nailed down, here are the two important

websites that you need to remember... not so much the second one, but the first one.

We will use the first website to figure out what is the starting tractive effort that

is required to achieve an acceleration rate of 2.5 mph/s for the R32. The second site

is simply used to convert between meters/second squared and km/h/s, since the first

site calculates acceleration in meters/second squared.

After inputting the numbers, we have our starting tractive effort for the R32.

Recall in a different tutorial for TS2015, where I show how to modify train physics

for acceleration, I give you the method to determine the relationship between power

and tractive effort. Let's see if I can pull that up real quick... Well, it seems I did

not save that text file; oh well. I'll just type out the formula really quick again:

Tractive Effort (kN) = [Power (kW) * 3.6] / Speed (km/h)

or as an example (ACS-64 TE @ 201.125 km/h given 6400 kW):

114.56 = (6400*3.6)/201.125

114.56 kN of TE is produced by the ACS-64 @ 125 mph given a power rating of 6400 kW.

Now, given that equation, we can use it to determine the maximum speed at which the R32

can sustain 2.5 mph/s acceleration given its power rating of 115 hp per traction motor.

See if you can follow along...

By plugging in the power rating per car and the calculated starting tractive effort,

we can calculate the point where continuous max power is achieved; at any speed point

lower than the calculated point, acceleration will remain @ 2.5 mph/s, while at any

speed point higher than the calculated point, power will be constant, but acceleration

will decrease.

You now have all you need for coding in acceleration physics in openBVE. Let me

demonstrate. I have the R32 already loaded into the train editor...

You will notice that after the constant acceleration range has been set, you still need

to determine how quickly the acceleration drops off. For the sake of this demonstration

we will set balancing speed at 55 mph (88 km/h). You must manipulate the e(2.0) value

so that the right end of the acceleration curve meets the bottom of the graph @ the desired

X-value (in this case, 88 km/h). A higher e value will result in a lower balancing speed,

and vice versa. That is basically what you need to do. I will now perform the calculations

for the remaining stock I have listed below using the same process. Just follow along

if you need more clarification.

In actuality, it is possible to calculate the speed point where near 0 TE is generated,

which would indicate the actual balancing speed, minus the train resistance. In order to

properly determine balancing speed, you must calculate the train resistance value (kN).

But that is for another time.

Now, GRANTED, these calculated values are for the MAXIMUM *POTENTIAL* acceleration curve.

The actual acceleration curve in real life can be programmed at lower values by

the Transit Authority (to conserve power / enhance operational safety margins). This is

especially true of the NTT rolling stock.

Thanks for watching, hope this was informative and that you guys learned something

new today =)