train acceleration vs horsepower

[dehusman]

gregc

Randy pointed out why a 1000 HP switcher is adequate to move entire trains at slow speed in a yard. And the plots showed the need for a 3000 HP locomotive to get a train up to speed quickly when a 2000 or 1500 HP engine could also achieve the same speed.

Its not that you need a 3000 hp locomotive, its that you need 3000 hp.  Two 1500 hp or one 3000 hp engine would have similar acceleration rates for a light to medium sized train.  For a very heavy train, 2 1500 hp engines would have better acceleration because they have twice the axles so can apply a higher % of their power to each axle without slipping. 

[gregc]

dehusman

The Reading Co. tested using 1000 hp NW-2's on commuter trains and while they could reach speed, they couldn't accelerate fast enough to maintain schedule, the RDG went with FP7's instead.

When practical railroad men hear the size of cylinders, the diameter of driving-wheels, and the boiler dimensions of a locomotive, mentioned, they understand what kind of service the engine is adapted for, and about the weight of train it can haul.

i don't have the experience of many of you.   This is why i generated the plots which i feel show the effect of varying amounts of horsepower on train speed and acceleration.   I believe they account for the maximum TE due to adhesion, the decreased TE as speed increases with constant horsepower and the effect of train resistance as speed increases resulting in non-constant acceleration.

Randy pointed out why a 1000 HP switcher is adequate to move entire trains at slow speed in a yard.   And the plots showed the need for a 3000 HP locomotive to get a train up to speed quickly when a 2000 or 1500 HP engine could also achieve the same speed.

 

[gregc]

i was grossly wrong when I said "that the leverage between the piston and wheel can vary (Johnson bar?)".   (yet another learning experience)

i've read about cutoff.   But I found the Tractive Effort Calculator confusing when changing the cutoff also changed the Weight on Drivers and there was no setting for speed.

unlike a diesel locomotive where you dial up the power to the motor, it seems that a steam engine is more like a fuel injection on a car.   The Bosch system i'm familiar uses a constant pressure fuel system and controls the fuel amount by controlling the time the injectors are open.

it seems that cutoff controls the power to the cyclinders by controlling how much steam is allowed to enter.

selector

... the piston slows, stops, and then returns in the other direction, now accelerating in front of another wavefront of admitted steam.

it also makes sense to me that cutoff is necessary as speed increases to limit steam entering the piston to the beginning of the stroke where its effect is maximized and to limit the pressure in the cyclinder at the end of the stroke to make it easier to be forced out of the cyclinder when it reverses direction.   

An engineer obviously has to get a feel for this and I assume that in order to maximize power/acceleration the cutoff has to be reduced as speed increases until it is reduced further to simply maintain speed.   Presumably the fireman had stopped adding fuel to the firebox before reaching the desired speed anticipating the reduced need for steam.

 

acceleration and speed depend on drawbar force (== tractive effort).   I believe the plot of diesel vs steam horsepower provides a comparison for determining acceleration for a steam locomotive.   I assume the steam plots represent what a well operated steam locomotive is capable of doing.    This obviously depends on the proper use of cutoff.

[BRAKIE]

ATLANTIC CENTRAL

I have never cared for using any throttle with momentum, DC or DCC.

Sheldon,Momentum has always been a favorite mode for me since I like realistic switching.

 

Another favorite thing was pulse power on MRC's Golden Throttle pack of the early 60s since it slowed those old open frame motors down.Today I use momentum and speed step on my GP7/9s and just speed steps on my Alco RS-1,RS-3 and RS-11.

[BRAKIE]

dehusman

If you have an ISL, then it matters even less because below 20 mph the acceleration rate is more determined by the electrical gear and turbocharger than the hp. For example GE's accelerate really slow.

And if you use older GP7/9s you have the EMD lag in transistion even when switching whereas Alco RS-1 ,RS-3 and RS-11 has instant throttle response.

IMHO  Geep 7/9s on a ISL demands monmentum with speed step for closer to prototype operation.

[dehusman]

Fun fact:

The Reading Co. tested using 1000 hp NW-2's on commuter trains and while they could reach speed, they couldn't accelerate fast enough to maintain schedule, the RDG went with FP7's instead.

[selector]

Greg, the cut-off changes afforded by the reverser (whether powered by air or the lever called the Johnson Bar) do nothing for adhesion or mechanical advantage.  The cut-off is merely the limitation of the admission of steam while the piston is moving ahead of the pressure imparted by the steam.  With full cut-off, often down to 15% of the duration of movement of the piston, or its length of stroke, take your pick, the valve leaves the port open for a very short duration.  This is used at speed when piston motion is rapid and the cycling rate is near or above 4 cycles per second.  This conserves fuel because the boiler doesn't have to supply all the steam that can occupy the full volume of the cylinder once the piston slows, stops, and then returns in the other direction, now accelerating in front of another wavefront of admitted steam.  With 15% cut-off, the valve admits very little steam that must then expand and fill the increasing volume behind the advancing piston.  

When 'lifting' a train, a steam locomotive is typically going to need a more constant pressure applied to the advancing cylinder so as to fill the expanding volume, so the reverser is positioned to allow the valve to admit steam for a much longer time.  In many cases, up to 85% of the piston's stroke.  This keeps the pressure high, as opposed to what happens when the cut-off is only 20% and the limited steam must expand to fill the void.  Understandably, at 20% cut-off the steam's pressure drops quickly in front of the advancing piston.  This is just sufficient to impart a continuance of momentum if the track conditions and rolling conditions don't change for the train.

What would change the gearing for the locomotive would be the length of the main crank, or the diameter of the drivers, neither which change.

Steamers produce their highest horsepower between 3-4 cycles per second.  A 6000 hp Niagara isn't going to be providing that to the pistons when it is running at 80 mph.  But it will be providing much more HP to motive effort at 70 mph than a diesel will, the latter having fallen off near the 40-50 mph mark, depending on gearing and other factors.  At least, that is what respected authors on the subject have related to their readers over the years.

[gregc]

less dramatic reduction in TE for steam.  > hp and TE for steam at higher speed.

[gregc]

dehusman

It doesn't.

are we looking at the same calculator?

http://steam.wesbarris.com/misc/tractiveEffort.php

changing the cutoff changes the field that says "Weight on Drivers"

i understand that for a given weight, there is a max TE that can't be exceeded due to adhesion.

i expected increasing the cutoff to change, possibly increase the TE up to some max.

[gregc]

dehusman

Correct.  If you compress the curves due to shorter distances and times, the curve "disappears".

of course the curves are going to compress if i use an 1800:1 fast clock.   

I've run trains with so much momentum that they take 15+ seconds to get to top speed.   All profiles rapidly get to half top speed in < 5 secs.

dehusman

Also I think you are misunderstanding "full speed".

not suggesting max loco speed but the desired top speed of the train.  of course different trains run at different speeds.   

But the 1000 HP profile demonstrated that the max speed was limited due to the limited horsepower and train tonnage

dehusman

The problem is how do you vary the speed curves depending on the train?

i'm not suggesting changing the speed curves.

i'm suggesting that the current DCC implementation of momentum with constant acceleration is not realistic.

it's not obvious how it can be improved (changing the speed curves for different train seems impractical)

dehusman

The curves really don't have anything to do with the locmotive, it has to do with the hp/tt of the train.

I thought it was made clear that each plot (profile) depended on HP and train tonnage

dehusman

The only way to vary the acceleration and make it look right is to assign engines to a specific train and adjust the acceleration for that train.

it was suggested that that it could be implemented in a throttle if the HP were specified for the loco(s) and tonnage specified for the train.   The throttle sends the appropriate speed step to follow the profile.   This could work as long as the loco did not loose power since the profile would only depend on time.

the ProtoThrottle code has a feature to enter train tonnage as a future feature.

[dehusman]

gregc

i don't understand why changing the cutoff affects the weight on the drivers? (how does it change the weight of the locomotive)?

It doesn't.

You are over simplifying.  There is a factor of how much power the locomotive can transmit to the rails without slipping.  That is a function of speed, weight on drivers and wheel slip.  That's why a high speed, high horsepower engine is a pig at low speed (until AC engines).  That's why the PRR T-1 4-4-4-4 wa a "slippery" engine.  It had so much power it could easily exceed its adhesion and spin the drivers.  That why AC engines and modern DC engines are so much more powerful than equivalent hp engines of decades ago.  They have so much better wheel slip control.

[dehusman]

gregc

if you used a 1800:1 fast clock - 1 sec == 30 mins, then all trains would immediately jump to full speed (i.e. 23 mph for the 1000 hp case). Is this what your suggesting.

Correct.  If you compress the curves due to shorter distances and times, the curve "disappears".

Also I think you are misunderstanding "full speed".  The top speed of a 1000 hp road engine is somewhere in the 50-70 mph range (depending on gearing.)  The top speed of 1000 hp switch engine is typically about 45 mph, that's due to truck suspension, not horsepower.

  i'm suggesting that instead of using constant acceleration to full speed over the number of seconds resulting from the DCC CV3 value, that for hp limited trains, the speed should increase rapidly at first but then much more slowly. that profile depends on the hp of the loco (or combined hp of the consist) and the tonnage of the train. I've mentioned 3 profiles

The problem is how do you vary the speed curves depending on the train?

The curves really don't have anything to do with the locmotive, it has to do with the hp/tt of the train.

You have two sets of 3 SD40's.  Same hp, same gearing, same tractive effort.  You put one set on a 10,000 ton grain train.  Its going to accelerate more like the  "2000 hp" curve.  It will max out at about 50 mph.  Take the other set and put it on a TOFC train.  It will accelerate like the "3000 hp" curve.  

Same engines, same power, differnt curves.  Put 3 GP40's on the intermodal train and it will accelerate even faster.  Same hp, better acceleration.

If you put six 1500 hp GP-7's on the intermodal train it will accelerate like the "3000 hp" curve.

The only way to vary the acceleration and make it look right is to assign engines to a specific train and adjust the acceleration for that train. 

If you have an ISL, then it matters even less because below 20 mph the acceleration rate is more determined by the electrical gear and turbocharger than the hp.  For example GE's accelerate really slow.

[gregc]

ATLANTIC CENTRAL

http://steam.wesbarris.com/misc/tractiveEffort.php

i understand that max tractive force, which depends on coefficient of friction, is simply a fraction (~25%) of the weight on the drivers

i don't understand why changing the cutoff affects the weight on the drivers?   (how does it change the weight of the locomotive)?

and tractive effort is proportional to cutoff (why not always set cutoff to 100%)?    (I thought there was an optimal setting depending on speed)?

[ATLANTIC CENTRAL]

gregc

 

 

ATLANTIC CENTRAL

What about steam vs diesel?

 

 

i'm curious too.

i'm trying to get a handle on horsepower, TE and acceleration.   I believe i understand most of the Krug note, at least it makes sense to me.

i assume one difference with steam is that the leverage between the piston and wheel can vary (Johnson bar?).     I don't know if horsepower is constant on a steam locomotive.   that's another study

 

OK, first, a Johnson bar is the manual control that controls the cutoff rate, and puts the locomotive in reverse. Along with the throttle it controls the application of power after the locomotive is moving.

In real general terms, HP is not so important with a steam loco. Tractive effort and factor of adhesion mean much more in terms of its abilty to start a load and reach a given speed.

You can start learning more here:

http://steam.wesbarris.com/misc/tractiveEffort.php

 

[gregc]

ATLANTIC CENTRAL

What about steam vs diesel?

i'm curious too.

i'm trying to get a handle on horsepower, TE and acceleration.   I believe i understand most of the Krug note, at least it makes sense to me.

i assume one difference with steam is that the leverage between the piston and wheel can vary (Johnson bar?).     I don't know if horsepower is constant on a steam locomotive.   that's another study

[gregc]

selector

These might help you: https://dccwiki.com/Back_EMF http://www.sumidacrossing.org/ModelTrains/ModelTrainDCC/DCCDecoders/BEMF/ http://www.members.optusnet.com.au/nswmn1/y_qsi-back_emf.htm

i believe i understand BEMF, it is the counter current/voltage generated by an armature turning in a magnetic field proportional to motor rpm.   I understand that it can be used to determine if a motor is turning, its direction, as well as speed.

dcc momentum is currently implemented by simply increasing the speed step after a delay specified in CV3.   

why do you think the speed profiles i ploted can only be implemented using bemf instead of simply assuming a linear change in speed with each speed step and varying the delay with each change in step?

[ATLANTIC CENTRAL]

I forgot one other question/thought?

What about steam vs diesel? In my world I model both, yet in the real world the difference between electric traction, and mechanical traction is vast.

As commented above, a diesel may start a train and run out of power to accelerate it.

But generally, a steam loco can pull at speed any load it can start, limited only by its boiler capacity and its mechanical design tolerance that limits maximum speed.

Great, just what a DCC throttle needs, one more button labeled "steam or diesel".

More on tractive effort here:

http://webspace.webring.com/people/ib/budb3/parts/ste.html

Sheldon

[ATLANTIC CENTRAL]

A few last thoughts:

I have never cared for using any throttle with momentum, DC or DCC.

And one of my dislikes of many DCC throttles are encoder wheel throttle knobs.

So maybe pulse width modulated DC radio throttles, with its ability to provide constant brighness headlights before motion, a reasonable acceleration curve, and reliable slow speed is not so "dated" after all.

But I have never been concerned with having the "latest thing", just with having stuff that works well for my needs.

Sheldon

[ATLANTIC CENTRAL]

doctorwayne

Al Krug did a nice article on tractive effort vs. horsepower.  Unfortunately, I can't seem to find it on-line.

I have a copy of it, but it's rather lengthy and perhaps it's not suitable that I re-post it, as it's not my material. 

A more thorough on-line search may get you better results than my quick look.

Wayne

 

This one:

http://hm.evilgeniustech.com/alkrug.vcn.com/rrfacts/hp_te.htm

Al's site is down, this guy has mirrored it.

I don't really have an opinion here since I don't use DCC.

Even with the momentum feature turned off, my Aristo throttles have an "acceleration rate" that is not instant. Being a push button throttle you must hold the "FAST" button for a period of time to achieve full speed.

I have never mapped it to see if it is linear or not, but my natural sense is that it is not. And that by default, the pulse with modulation circuit of the Aristo throttle already provides the effect Greg is looking for.

Sheldon

[selector]

gregc

 

...while BEMF can accurately measure speed, it is not necessary for more realistic behavior unless there are severe mechanical issues with the model loco or you're interested in a very accurate speed profile.  

 

Simply setting the motor voltage for more realistic speed at a more realistic time should be more than adequate.

 

 

These might help you:

https://dccwiki.com/Back_EMF

http://www.sumidacrossing.org/ModelTrains/ModelTrainDCC/DCCDecoders/BEMF/

http://www.members.optusnet.com.au/nswmn1/y_qsi-back_emf.htm

 

[gregc]

dehusman

Now graph those same speed curves on the SAME time scale.  You end up with a square wave.

i don't understand why

you mentioned a square wave in your frist response where all the plots were on the same time scale: minutes.

dehusman

If you compress these curves to account for shorter model running distances or fast clocks what you will end up with is essentially a square wave, all the acceleration in the first little bit, essentially a jack rabbit start.  That totally defeats the purpose. 

if you used a 60:1 fast clock, the scale of the plots would be seconds.

if you used a 1800:1 fast clock - 1 sec == 30 mins, then all trains would immediately jump to full speed (i.e. 23 mph for the 1000 hp case).   Is this what your suggesting.

not withstanding the case above, I don't see how time scale affects the profile.

 

i'm not suggesting modeling prototypical increases in speed that take minutes.

i'm suggesting that instead of using constant acceleration to full speed over the number of seconds resulting from the DCC CV3 value, that for hp limited trains, the speed should increase rapidly at first but then much more slowly.

 

that profile depends on the hp of the loco (or combined hp of the consist) and the tonnage of the train.   I've mentioned 3 profiles

[dehusman]

gregc

in terms of time, simply rescale the time axis in seconds instead of minutes: ~5 sec for the 3000 HP loco to get to 30 mph, 8 sec for the 2000 HP loco and ~20 sec for the 1500 HP loco. on the following plot I added curves using CV3 settings of 5, 9, 25 and 40 where the x-axis for these curves is in seconds. If modelers are willing to use CV3 value similar to these, then the more realistic plot times in seconds should be acceptable on many layouts.

Now graph those same speed curves on the SAME time scale.  You end up with a square wave.

The other thing to realize in all this is that railroads power their trains up to certain horsepower per trailing ton based on the TRAIN not necessarily an engine.

If there is a 5000 ton grain train it might get 2500 hp.  If its a 5000 ton manifest train it might get 5000 hp.  If its a 5000 ton intermodal train it might get 12,000 hp.

If you put 2 GP40's on a 5000 ton manifest train, and 8 GP7's on an 5000 ton intermodal train, while a single GP7 has a slower acceleration curve, I guarantee that the intermodal train will out accelerate the manifest train.  The acceleration curve of a TRAIN is the sum of the horsepower of the engines (actually its more complicated).

If you program a 1500 hp engine to top out at 30 mph, that's baloney.  Early 4 axle units were (F3-F7-GP7-RS2-RS3-FA1-FA2) were nominally 1500 hp and easily handled trains at speeds up to 60-70 mph.  The ATSF used 1500 hp engines on its premier transcontinental passenger trains at very high speeds with rapid acceleration.

A railroad powers a TRAIN to the achieve the acceleration it needs for that TRAIN. 

Some railroads have gone away from horsepower/trailing ton (hp/tt) and have gone to a tons per powered axle (TPA).  A "powered axle" represents a specific amount of tractive effort and engines are rated at how many "axles" they have.  A C44AC might represent 10 axles, while an SD40 is 6 axles.  Power on a TRAIN is managed by TPA.  A grain train might get 500 TPA and an intermodal train might get 125 TPA.

Dave Husman

recovering Director of Locomotive Utilization

[gregc]

i had asked for confirmation of the plots.  No one seems to dispute their accuracy.   Thanks for the link to the Krug page.   I believe the plots are consistent though Krug is more focused on a train going up a grade which is a bigger deal.

the goal is to recognize how prototypical trains actually behave

rrinker

Realistic yes, but there's going to be a limit. Imagine you had unlimited room and really could put 50, 100 scake miles of track between towns. How many people would actually do such a realistic op session where at proper scale speed

dehusman

The largest layout in my area is ironically part of this territory and has maybe about 10 scale miles of track.  That means that with "prototypical" acceleration, the train would NEVER reach full speed. 

of course most modelers can't realistically model the distances and train lengths of real railroads.    but the ProtoThrottle suggests that many want to model the behavior more realistically.   I don't believe constant acceleration is realistic.

in terms of time, simply rescale the time axis in seconds instead of minutes: ~5 sec for the 3000 HP loco to get to 30 mph, 8 sec for the 2000 HP loco and ~20 sec for the 1500 HP loco.

on the following plot I added curves using CV3 settings of 5, 9, 25 and 40 where the x-axis for these curves is in seconds.   If modelers are willing to use CV3 value similar to these, then the more realistic plot times in seconds should be acceptable on many layouts.

but again, it's not the length of time, but the speed profile that makes it more realistic, depending on hp and tonnage.

selector

BEMF is very much needed for our decoders to meter out the proper voltage to the drive mechanism so that acceleration and deceleration are prototypical

while BEMF can accurately measure speed, it is not necessary for more realistic behavior unless there are severe mechanical issues with the model loco or you're interested in a very accurate speed profile.  

Simply setting the motor voltage for more realistic speed at a more realistic time should be more than adequate.

 

rrinker

My reasoning for using BEMF is that the decoder could automatically know the 'tonnage' of the train it was pulling.

i agree that specifying tonnage is a headache.   But I think using BEMF is not straight forward

• when should it be measured to determine tonnage?
• how does it distinguish between an increase in the length of the train vs the train going up/down a grade? (delta threshold)
• how accurately can it determine tonnage in terms of # of cars accounting for varying wheel resistance on cars (how big an effect is it on BEMF)?

i can see how using BEMF in a yard during switching might be necessary (maybe an option)

 

if the plots are recognized as being accurate and there is a desire to improve realism, then i believe it will take more than just a tweak to the CV3 setting (assuming you means to implement something either in a decoder or cab).   

The profiles are the result of limited HP resulting in decreasing tractive effort with speed and train resistance that increases with speed -- their difference

it looks like there are 3 interesting profiles

• excessive HP where the profile is basically linear (3 and 2000 HP)
• less excessive HP where speed increases rapidly initially but reaching full-speed is delayed (1500 HP)
• limited HP such as in a switcher where max speed is significanly limited depending on tonnage (1000 HP)

[selector]

OP wrote: "...BEMF isn't necessary unless you want to account for grades.   The current speed step is known to the decoder..."

This is incorrect.  BEMF is very much needed for our decoders to meter out the proper voltage to the drive mechanism so that acceleration and deceleration are prototypical, and so that the drive responds accurately to the speed table's parameters as the drive mechanisms running characteristics change with lubrication, operating temperature later in the session when the drive loosens, and to account for gear lash and wear over time.

[doctorwayne]

Thanks for that link, Jim.  All that was coming up for me was dead-ends.

Wayne

[BigJim]

doctorwayne

Al Krug did a nice article on tractive effort vs. horsepower.  Unfortunately, I can't seem to find it on-line.

I have a copy of it, but it's rather lengthy and perhaps it's not suitable that I re-post it, as it's not my material. 

A more thorough on-line search may get you better results than my quick look.

Wayne

Al Krug's Home page: 
https://web.archive.org/web/20150205123806/http://www.alkrug.vcn.com/home.html

[BRAKIE]

Jst for a fun fact..The majority of the engineers I worked with was more concern over locomotive  tonnage rating vs. tonnage of the train.

I suspect they figure they could get the speed up once they begin moving.

On my ISLs I use momentum and speed step.

[dehusman]

OldEngineman

Running the Conrail SEOP (Selkirk-Oak Point) some nights, with a longish train (say, 120 loads), on the table-top flat Hudson line going south, the engines would be in the 8th notch continuously and it would take 15 miles to begin to edge up close to track speed (50mph). That was with 3 B23-7's, all they gave you for that run.

The largest layout in my area is ironically part of this territory and has maybe about 10 scale miles of track.  That means that with "prototypical" acceleration, the train would NEVER reach full speed.  There is less than 15 miles, plus at some point the train would have to start to decelerate because it would run out of model railroad and would have to stop.

There is also the consideration of the the dynamics of the actual model train.  A model car weighs lets say 5 oz.  If it represents a load it weighs 5 oz.  If it represents an empty it weighs 5 oz.  A real car weighs maybe 30 tons empty and 130 tons loaded, roughly 4x the weight of an empty.

The speed curves are neat, but they only work when you match them to the weight of the train.  What weight are you going to use for the train?  If John runs 3 SD60's on the point of his 15 car "loaded" grain trains because that's the sizee for his layout space and Jim runs 3 SD60's on the point of his 25 car "loaded" grain train because that's the size for his space, are you expecting them to operate the same?  They both represent the SAME train, a loaded unit grain train.  What train weight are you going to tell the system to use to figure the acceleration?  15 model cars?  25 model cars?  15 real cars?  25 real cars?  100 real cars?

John's layout has only 3 miles of main track.  The grain train will meet 2 other trains along the way.  That means it will only go about 1 mile before it has to stop.  That means that one third to one half of each leg is deceleration. If it takes a real train 10 miles to accelerate to 50 mph, and John only has one half to 2/3 mile to accelerate, what speed will his trains reach?

If you compress these curves to account for shorter model running distances or fast clocks what you will end up with is essentially a square wave, all the acceleration in the first little bit, essentially a jack rabbit start.  That totally defeats the purpose. 

The only way to make it "prototypical" on a model railroad is to make something not match the model scenario.  Either the speed curves have to be changed, the "horsepower" of the engines altered or the "weight" of the train altered to fit the specific situation.  At that point its art not science, the acceleraton of the curve is adjusted to match whatever the observer thinks looks "prototypical".  It has NOTHING to do with the actual physics of the situation.

 

[rrinker]

 My reasoning for using BEMF is that the decoder could automatically know the 'tonnage' of the train it was pulling. Versus the somewhat unrealistic action of keying it in the throttle (which could just program the decoder)

 Realistic yes, but there's going to be a limit. Imagine you had unlimited room and really could put 50, 100 scake miles of track between towns. How many people would actually do such a realistic op session where at proper scale speed it takes you an actual 8 hours on your feet walking along with the train to get from the starting point to the destination? That would get old, real fast.

 Hence a fast clock, even a moderate one, compressing the 15 miles of a real train getting up to speed to fit within what can be realisticlly built - even then it's too much to try and simulate that accurately. At a 4:1 clock ration, it woult take 1/4 the time, 1/16 the distance - but how many layouts have even that much room even. At best, you'll just reach speed when it's time to brake for the next stop. At worst, you'll be in the next town before even getting close to speed. Which is why I think using momentum, and maybe a non-linear speed table, is about as good a simulation as you are going to get int he confines of model space.

 That does result in decidely non-linear acceleration. While the accel and deccel CVs are linear, setting a static time for changing from one speed step to another, if the speed curve is non linear so that each step is not an equal increment in speed, then you have made a non-linear acceleration curve. Because of the single factor nature of the momentum CV, the speed curve might have to be more exaggerated than it would be if no momentum were in use. Short of adding a second table that controls the momentum for each speed step, that's the only current option and probably close enough, given all the other limitations in the model world. 

                                   --Randy