calculating RPM from road speed and gear ratios when you have no tach

[Thorin]

I have a 1995 Dodge Colt.  It is a re-badged Mitsubishi Mirage.  In the US they stopped selling Colts as of 1994, but in Canada they went one more year into 1995.  Mitsubishi Mirages are not very common, and Dodge Colts from 1995 are hard to find.

Anyway, my son started driving this car.  It's a standard but it does not have a tachometer, so you have to guess what RPM you're at by engine sound and feel.  I drove it for years like that, but now he was wondering when to shift and my first instinct was to tell him to keep the RPMs below 3,000.  Of course, he has no idea when 3,000 RPM happens, as there's no tach.

So I thought I'd look up the gear ratios and final drive (aka diff) ratio, and then just work out the speed at a given RPM based on the tire diameter (which I do know).

Okay, it was nearly freakin' IMPOSSIBLE to find this information.  Gear ratios, you'd think they'd be easy to find, right?  Well, no, not for this type of car from this type of vintage.  I finally found a Mitsubishi Mirage transmission shop manual (shows you how to rebuild the tranny from start to finish), which happened to list the gear ratios and final drive ratio.  I still had to decipher other codes to know exactly which transmission and which set of ratios.  The manual was here: http://www.lilevo.com/mirage/Manuals/FWD%20Manual%20Transmission%20F4M21-F5M2X-F5M3X-W5M3X%20Series%20PWEE8902-ABCD%2022A.pdf

This is for a 1005 Dodge Colt / 1995 Eagle Summit / 1995 Mitsubishi Mirage with a 4G15 motor and a F5M21 4021 transmission.
1st:  3.363:1
2nd:  1.947:1
3rd:  1.285:1
4th:  0.939:1
5th:  0.756:1
reverse:  3.083:1
final drive:  4.021:1

Note that officially this has two overdrive (or more precisely, overgeared) gears, 4th and 5th.  4th and 5th are both at less than 1:1 ratio.

So how did I figure out RPM from tire diameter and gear ratio and final drive ratio?  Here's the math:

Convert RPM (revolutions per minute) to R/s (revolutions per second).  Determine reduction in revolutions due to gearing.  Figure out the tire diameter in millimeters.  Multiply reduced revolutions times tire diameter to get the distance travelled for said revolutions.  I'll do a sample for first gear:

2,400 RPM / 60 s / M = 40 R/s
40 R/s / (3.363 x 4.021) = 40 R/s / 13.522623 = 2.958 R/s <-- this is how many revolutions the tires will make when the engine makes 40 revolutions
P155/80R13 tires
- diameter: (155mm x 80% x 2) + (13inch x 25.4mm/inch) = 578mm diameter
- circumference: 578.2mm diameter * PI = 1,816mm/R circumference <-- for every one revolution of the tire, this is how far the car moves
2.958 R/s x 1,816 mm/R = 5,372 mm/s
5,372 mm/s x 1 km / 1,000,000 mm x 3,600 s / 1 h = 19.34 km/h

So at 2,400 RPM in first gear, the car is moving about 20 km/h, give or take some rounding (since tire diameter changes a little due to air expansion/contraction).  Or to put it the other way, like I was looking for, at 20 km/h in first gear, the engine is doing 2,400 RPM.

Now I took all this lovely math and put it in a spreadsheet, then just repeated the same calculation (copied and pasted of course) for every 500 RPM from 500 to 7,000 (which I learned is where the rev limiter kicks in, so the engine won't go any faster), and it showed me why I can get up to about 57km/h in first gear, and about 96km/h in second.

Hopefully someday this will be useful to someone who is trying to figure out how fast their engine is going without having a tachometer on board.

And I should make a little cheat sheet to stick to the dash to convert typical speedo km/h into engine RPM for each gear.

[Lazybones]

Other than avoiding red lining the engine when trying to rapidly accelerate I don't think I have ever used the tach under normal driving conditions and speeds.

Then again I drove without a working speedometer for over a year once so I might not be the best to ask if it is important.

[Thorin]

lol

I have had tachs in all but two cars, both of those were standards where you want to know the RPM so you know when to change gears.  To save on gas, smaller cars I keep under 3,000RPM during acceleration, big engined vehicles I keep under 2,500RPM.  That's pretty sedate driving, mind you, and most people will then beat you off the line if you start at the same time.  But hey, accelerating from a traffic light that just turned green is where a large portion of your gas gets burned off.

At the same time I like to know what the outer limits of my vehicles are and have redlined every single one of them.  Even the brand new one.

Anyway, the hardest part of all of that was finding the damn gear ratios.  Seriously, there's very little info on the web about my vintage and make and model of car.

[Lazybones]

both of those were standards where you want to know the RPM so you know when to change gears

My comment of not using the tach applied to standards I have driven (automatics rarely have them), I really don't glance down at the tach when driving a standard unless something sounds funny.

I suppose the first time driving a particular standard I sometimes look, but mostly I figure it out by sound and feel.

[Thorin]

Hmm, all the automatics I've ever driven, including rentals, have had tachs.

[Melbosa]

Could add a tach for very little money and not much experience with engines.  Sell them at princess auto, crappy tire, etc...

[Lazybones]

Hmm, all the automatics I've ever driven, including rentals, have had tachs.

hmmm, maybe I am just waxing nostalgic on specific automatics I owned.  My Mazda 5 is automatic and has one, but it also has that semi manual mode where you can flip through the gears.

[Thorin]

Could add a tach for very little money and not much experience with engines.  Sell them at princess auto, crappy tire, etc...

Where's the tach wire hook up on a 1995 Dodge Colt / Mitsubishi Mirage? I had a hard enough time finding the gear ratios.

[Thorin]

Hmm, all the automatics I've ever driven, including rentals, have had tachs.

hmmm, maybe I am just waxing nostalgic on specific automatics I owned.  My Mazda 5 is automatic and has one, but it also has that semi manual mode where you can flip through the gears.

I find "manu-matic" a pretty useless invention. There's too many times when your gear selection gets overridden by the computer plus when it does gear down to a lower gear there's a jerk on the drivetrain because it doesn't match the engine speed to the tire speed. At least with a real standard you can speed up the engine, slip the clutch a little, or whatever you need to do to not be jerky in driving.

[Lazybones]

Hmm, all the automatics I've ever driven, including rentals, have had tachs.

hmmm, maybe I am just waxing nostalgic on specific automatics I owned.  My Mazda 5 is automatic and has one, but it also has that semi manual mode where you can flip through the gears.

I find "manu-matic" a pretty useless invention. There's too many times when your gear selection gets overridden by the computer plus when it does gear down to a lower gear there's a jerk on the drivetrain because it doesn't match the engine speed to the tire speed. At least with a real standard you can speed up the engine, slip the clutch a little, or whatever you need to do to not be jerky in driving.

O I don't disagree..

Also some goggling seems to indicate that much like power windows and locks they put the tach on just about all cars after 2000 ish... Before then there where even some manuals that didn't come with them.

[Thorin]

Yes, I have one

New vehicles do have some nice new tech.  Handy new tech on my Silverado Crew Cab:

Hill Assist: If you're facing uphill and stopped and in a forward gear, when you take your foot off the brakes the brakes stay clamped until you start pushing the gas pedal or two seconds have elapsed; I've tried it and it's smooth.  I think the same happens if you're facing downhill but are in reverse.

Panic Brake Assist: If you jam the brake pedal hard, all brakes are squeezed as hard as possible until their ABS comes on.  If one tire has more traction than another, its brake will be squeezed harder.  This helps you stop faster in a panic stop situation, and is activated based on how quickly and how hard you push the brake pedal.  I've tested this already and I can't believe how fast I can bring a 5,400lb truck to a stop (in comparison, my little white car weighs 2,300lbs, or less than half).

Torque Management: God-damn torque management, most truck enthusiasts hate it.  TM reduces engine power just before the transmission shifts gears.  This makes the shift smoother and reduces strain on the drivetrain front to back, but especially on the transmission, thus making it last longer.  A side effect is that three to five year old trucks don't need new transmissions, so people who buy them used don't think they're pieces of crap (and thereafter avoiding that brand).  I happen to like it because I like a smooth shift more than a sharp shift, and I like the idea of not needing a new transmission in five years.  TM also depowers on initial acceleration from a stop, which means it's hard to spin the tires.  By the way, manuals have a manual type of torque management - most people take their foot off the gas pedal when changing gears and let the clutch out smoothly instead of just popping the pedal back out.

Traction Control: Limits wheelspin by applying brakes on wheels that are spinning.  If I'm 4x4ing I can turn this off with a button on the dash, plus it turns off automatically if I go into 4Lo.  I've played with turning this off and going into 4Lo, and I've had my tires on mud where they spun and the traction control kicked in.

Stability Control: Brakes certain wheels to try and recover the vehicle from a slide, whether oversteer (back end stepping out) or understeer (front end not turning enough).  Some other mud allowed me to test this (by accident), and I was amazed how quickly the truck went back to pointing in the direction I wanted to go.

Sway Control: It's a truck, it can pull trailers, trailers can start swaying from side to side.  A badly swaying trailer can tip on its side and drag the tow vehicle with it.  So Chevy put in sensors for sway, and if the trailer starts swaying then the vehicle is slowed down by depowering the engine (what a trained driver would do in the same situation).  They tell you to still install a proper sway control system, though, so that hopefully this set of sensors never needs to be used.

I'm surprised how many new programs are running on the PCM (Powertrain Control Module - the engine computer).  I hope none of them have bugs.

[Lazybones]

I'm surprised how many new programs are running on the PCM (Powertrain Control Module - the engine computer).  I hope none of them have bugs.

Well nothing is perfect, however with cars, the tech is very iterative... and they tend to reuse and extend the same feature over and over..

ABS evolved into Electronic Traction control, then stability control, etc and with each generation it seems to get better.

I drove several cars with early ABS and Traction control.. It is a whole lot smoother and quieter on my Mazda 5 than on the  90s OLDSMOBILE TORONADO I drove.. It used to be really loud when it kicked in and really pulsed the break peddle.

[Tom]

Yeah, if they get that software wrong enough, they are likely very liable for any incidents.

You know what I think they are doing? Getting us all ready for the robot take over.

1. start with a few handy subroutines,
2. then an almost ai like intelligence,
3. fully automatic driving
4. ??
5. ALL HAIL OUR ROBOT OVERLORDS!

[Melbosa]

Could add a tach for very little money and not much experience with engines.  Sell them at princess auto, crappy tire, etc...

Where's the tach wire hook up on a 1995 Dodge Colt / Mitsubishi Mirage? I had a hard enough time finding the gear ratios.

Usually near the Distributor or Ignition Coil.

[Lazybones]

Yeah, if they get that software wrong enough, they are likely very liable for any incidents.

You know what I think they are doing? Getting us all ready for the robot take over.

1. start with a few handy subroutines,
2. then an almost ai like intelligence,
3. fully automatic driving
4. ??
5. ALL HAIL OUR ROBOT OVERLORDS!

While google is already testing fully automatic cars, in the high end ones and so to trickle down to regular ones there are lots of new features.

Automatic braking
http://gizmodo.com/179961/volvos-fully-automatic-brakes

Active Park assist
http://www.youtube.com/watch?v=xW-MhoLImqg

Adaptive Cruise Control
http://auto.howstuffworks.com/cruise-control4.htm