Acceleration comparison ft. Distance Traveled

[RulerofRails]

Not being a math whiz, my understanding of acceleration was/is lacking. I had the feeling that comparing the acceleration levels as I did here, really doesn't give a good idea on the performance benefit/dis-advantage of the acceleration setting for a loco in terms of gain/loss of mileage covered in a given time.

From the RT3 manual:

Acceleration - Measures how fast this locomotive reaches top speed from a standing start.

I listed the amount of time needed to reach top speed for each level here. Repeated for easy reference:

Code: Select all

Hrs:   Level:
4   Instant
15   Virtually Instant
25   Ultra Fast
36   Very Fast
47   Fast
58   Above Average
69   Average
80   Below Average
90   Poor
101   Very Poor
112   Extremely Poor

*Hours slow-time are equivalent to half a normal-time day. So 1 month (normal) = 60 hours (slow).

Same data in a graph:

In my old explanations I used the term "linear" acceleration, but I believe the correct term is "constant" acceleration. In constant acceleration starting from standstill, during a given period of time an object will have an average velocity of approx. half of the final velocity (hope I got that right, sorry in advance to any math geniuses).

Since we know how long acceleration to top speed takes for a given level, we can translate this to say that a train accelerating to top speed is essentially traveling at top speed (for illustration assuming a flat-ground route, so this is constant for the entire journey) for HALF the period of acceleration.

From the list above we see that Above Average takes 58 slow time hours (half- normal days). Halve that to give 29, so during those 58 hours the train will travel approximately the same distance as 29 hours at top speed.

Compared to a train already maxed out at constant top speed (no acceleration time) here's the percentage of this distance covered by the various acceleration levels. Notice the scale is large enough to see 6-month journeys (360 half-days).

And finally a comparison to see the mileage advantage of a higher/faster acceleration level. This is once again expressed as a %.

***If anyone wants a spreadsheet that generates specific values or one with a range of most values in a big table. Let me know.***

For the purpose of comparing locos, we will see different top speeds. I'm not 100% sure, but I believe that the factor of benefit/disadvantage for differing acceleration levels can be calculated separately from the factor of benefit/disadvantage for outright speed differences.

What about grades?
Obviously, there are grades in a real game, which for one means that a maximum speed will be the target of acceleration instead of top speed. Any grade severe enough to cause deceleration will most probably will increase the amount of total time on a run that a loco is accelerating. Downhills are accleration boosts, but on the overall I believe a train on a graded route will be more affected by it's accleration rating than on flat-ground. Basically, my guess is that the higher/faster levels probably have somewhat more advantage on graded terrain. I don't think it's too much, so I'm not going to delve into details for that.

[Gumboots]

In my old explanations I used the term "linear" acceleration, but I believe the correct term is "constant" acceleration. In constant acceleration starting from standstill, during a given period of time an object will have an average velocity of approx. half of the final velocity (hope I got that right, sorry in advance to any math geniuses).

Important point here: this is true if, and only if, the "given period of time" is centred on the entire period from 0 to top speed.

IOW, it's true for a period from t=10% to t=90%, and it's true for a period from t=40% to t=60%, but it is not true at all for a period from t=10% to t=20%.

Which you probably know already, but I thought it should be stated clearly so there was no misunderstanding by anyone.

Haven't done any number crunching on your graph, but it looks about right. It does demonstrate the (known) advantage of a good acceleration rating for short hops on flat terrain.

[Just Crazy Jim]

My very rusty high school maths and physics find no fault with your formula.

That being stated, here are some ideas to consider.

I do remember that velocity (v) is the term used to express the speed of an object in motion at any given time. How this relates to Top Speed in-game may break the rules of physics. In the real world, a locomotive may exceed the top speed on a negative grade, I'm not sure that would be the case in RT3. From what I have seen, the top speed is the highest velocity a given locomotive can ever achieve. The issue being, that in a real world application, a locomotive that travels a course with equal amounts of positive and negative grades should approach a time/distance performance nearly equal to that of a similar locomotive traveling the same distance on a zero-grade track by merit of the locomotive being able to achieve otherwise impossible velocity on the down-grade. Obviously, the likelihood of a perfectly balanced amount of positive and negative grades is the wiggly part in that.

Also, in the RW, a locomotive that travels 1000 miles of purely negative grade should cover that distance faster than a similar locomotive that travels 1,000 miles on a zero-grade by means of constant acceleration due to the effects of gravity (gravitational constant or G). In fact, a locomotive on a purely negative grade of sufficient length should eventually achieve a top speed approaching (but never quite achieving) that of terminal velocity. This is not what I have seen demonstrated in RT3.

This is why I have stated in the past that I do not quite understand how the game handles negative grades. Certainly, I know what the effects are in-game, but the physics model of the negative grade doesn't quite follow a proper acceleration/velocity model that accommodates the RW behaviour of a heavily laden freight train on a negative grade. So, I have come to considered the in-game term "Top Speed" to indicate "maximum safe operational speed" and that this is strictly and artificially enforced with no regard to RW physics.

I would have to say that gravity in RT3 is not safely expressed by G. I am not sure if the physics model in RT3 even uses G.

[Gumboots]

In the real world, a locomotive may exceed the top speed on a negative grade, I'm not sure that would be the case in RT3. From what I have seen, the top speed is the highest velocity a given locomotive can ever achieve.

Yup. Trains in RT3 will never exceed the top speed defined in the.lco file, even if you send them straight off a cliff.

However, you can fake the effect of negative grades to some extent. The way you do it is by using a negative "free weight" value in the .lco file, with a top speed set to what you think it should do down a suitable grade. The negative free weight works the opposite to the usual positive values. Instead of allowing you to pull more cars at top speed, it only allows you to pull a negative number of cars before speed starts dropping. This means you will never see the defined top speed on flat terrain, but the boost given by a downhill grade will make it achievable downhill, as long as you balance the free weight value against expected length of grade, etc. It's a suck it and see sort of thing.

I am fairly sure (haven't tried to check) that the game uses exactly the same speed multipliers downhill as it does uphill, except that instead of multiplying by the speed reduction constants for that grade it divides by them. Or, if you prefer, it multiplies by the inverse. Which gives the effect of the train being faster downhill.

I would have to say that gravity in RT3 is not safely expressed by G. I am not sure if the physics model in RT3 even uses G.

Not likely. Can't see why it would.

[Just Crazy Jim]

In the real world, a locomotive may exceed the top speed on a negative grade, I'm not sure that would be the case in RT3. From what I have seen, the top speed is the highest velocity a given locomotive can ever achieve.

Yup. Trains in RT3 will never exceed the top speed defined in the.lco file, even if you send them straight off a cliff.

However, you can fake the effect of negative grades to some extent. The way you do it is by using a negative "free weight" value in the .lco file, with a top speed set to what you think it should do down a suitable grade. The negative free weight works the opposite to the usual positive values. Instead of allowing you to pull more cars at top speed, it only allows you to pull a negative number of cars before speed starts dropping. This means you will never see the defined top speed on flat terrain, but the boost given by a downhill grade will make it achievable downhill, as long as you balance the free weight value against expected length of grade, etc. It's a suck it and see sort of thing.

I am fairly sure (haven't tried to check) that the game uses exactly the same speed multipliers downhill as it does uphill, except that instead of multiplying by the speed reduction constants for that grade it divides by them. Or, if you prefer, it multiplies by the inverse. Which gives the effect of the train being faster downhill.

I never thought to go at it that way. Negative "free weight" sounds so utterly mad that I'll have to play with that.

I guess another way to look at the "Top Speed" is to gloss over the maths and say "Top speed = Terminal velocity".

I would have to say that gravity in RT3 is not safely expressed by G. I am not sure if the physics model in RT3 even uses G.

Not likely. Can't see why it would.

I guess you're right. It's just that my memory of physics class (all those years ago) involves a near endless emphasis on the gravitational constant and ciphering out the arc of everything from a toaster launched from a trebuchet to using the gravitational well of a gas giant to do a "slingshot" maneuver. I think Mr. Jenkins may have thought we should all be working for NASA.

[Gumboots]

I never thought to go at it that way. Negative "free weight" sounds so utterly mad that I'll have to play with that.

Personally I don't think free weight is a good name for it, but it's the name everyone was using for yonks before I started messing with this stuff. It's really just another speed multiplier, but the way it works is that if "free weight" = 1x cargo car weight you can haul 1 car at top speed on flat terrain. If it's equal to 8x car weight, you can haul 8 cars at top speed on the flat.

It has other effects too, but they're not obvious at a glance, so nobody noticed before I reverse engineered the formulae for speed on grades.

Anyway, since it's just another speed modification factor you can use it however you like.

[Gumboots]

Bumping this. Been thinking about acceleration ratings and how they affect performance in stop/start traffic. It's all very well having a theoretical curve, but in practice the actual rate of acceleration in mph/minute (or whatever units float your boat) is going to be determined by the acceleration rating and the nominal top speed with a given consist on a given grade. Taking RoR's figures from up the page:

Code: Select all

Hrs:   Level:
4   Instant
15   Virtually Instant
25   Ultra Fast
36   Very Fast
47   Fast
58   Above Average
69   Average
80   Below Average
90   Poor
101   Very Poor
112   Extremely Poor

If a loco has an acceleration rating of Poor, that's supposedly 90 hours (slow time) to Top Speed. Above Average give 58 hours (slow time) to Top Speed. If top speeds with the same consist on the same grade are equal then the loco rated Above Average will accelerate at 155.2% the rate of the loco rated Poor. However, if the loco that has a Poor rating also has 155.2% the top speed for the same consist and grade, then both locos will accelerate at the same rate, until the slower loco reaches its top speed for those conditions.

In stop/start traffic, like a heavily congested suburban network, what counts is what speed the loco can get to before being stopped again by another train or station. So to figure out the best loco for those conditions you'll need to figure out what speed your reference loco can usually achieve under those conditions, then compare its actual acceleration rate (in mph/minute) with whatever you're thinking of replacing it with.

Which is going to be pretty simple to calculate. As long as neither loco can reach its nominal top speed under these conditions, which is probably going to be the case 99% of the time, the formula is just [(Top speed Loco 2)x(Time to top speed Loco 1)]/[(Top speed Loco 1)x(Time to top speed Loco 2)].

If that formula gives an answer of 2, then Loco 2 will be twice as good off the mark as Loco 1. If it gives an answer of 0.9, then Loco 2 will be 10% slower off the mark than Loco 1. I'm thinking this should be added to the old speed vs grades spreadsheet, as an extra bit of useful info.