Do RPMs predict speed in a particular gear regardles of grade?

I have a Miata in hilly San Francisco with a manual transmission and my speedometer is broken.
However, my tachometer still works…and I have a standing argument with a pal of mine about how fast the car is going up and down hills.

I live on a pretty steep street with a 27% grade. (The steepest street in San Francisco has a grade of 41%.)
In first gear the engine has to work hard to climb my hill and the tachometer shows high RPMs.
I think the car is going significantly slower going up that hill than it does when it is in the same gear and at the same RPMs on a level street.

My pal argues that the RPMs will control, exactly and consistently, the car’s speed in a particular gear and at a steady RPM regardless of the grade or steepness of the road.
I argue that may be predictably true on a flat road, but the actual speed of the car depends on the grade, or steepness of the road. If the car went down a hill while kept in the same gear at the same RPMs as going up the same hill, it would be going faster, maybe much faster, than if it were going up that hill.
He counters that regardless of the grade, the engine, transmission and differential are all so tightly connected that the car’s speed MUST be consistent with the RPMs.

Do I need to fix the speedometer to end this argument or can you guys settle it?

Your pal is right. If you are in a specific gear, the rpm and the speed will be the same regardless of the grade. The only time it would be different on a manual shift car is if the clutch is slipping. I used to ride a intercity bus and there was no speedometer. The tachometer was marked in speed and had different colored bands for the 5 different speeds.

You friend is correct. And as Triedaq said…if it was different - it would mean the clutch or tires are slipping.

He counters that regardless of the grade, the engine, transmission and differential are all so tightly connected that the car's speed MUST be consistent with the RPMs. -

100% correct.

I did have a manual transmission car where the OP would be correct. That car was my 1948 Dodge. It had a fluid coupling between the engine and the clutch and would allow painfully slow high gear starts. It also allowed the driver not to have to depress the clutch at a stop sign. I think the fluid coupling did save wear on the clutch, but I drove the car as I would a conventional manual transmission car.

Your friend is absolutely 100% correct. The connections between the crankshaft and the tires are all totally mechanical, fixed ratios for each gear.

What does change is the amount of fuel you need, the amount of gas pedal pressure you need to apply, in order to keep a consistant speed in a constant gear. Going down the hill will require much less use of the gas pedal than going up, and taking your foot totally off the gas while descending may even be appropriate to keep the vehicle’s speed consistant.

The gas pedal does not control the engine’s speed directly in the sense that you’re thinking. It controls the amount of POWER the engine has available, the amount of ENERGY available to the engine. If your engine needs more power because you’re starting uphill, or because you’re accelerating, stepping on the gas pedal harder makes that power available. 30mph going uphill in 3rd will require the same engine speed as 30mph going downhill in 3rd, but it’ll need more gas to maintain the engine speed.

I think it’s hard to seperate the amount of gas you need to give the engine from the engine’s speed, but i this case it’s necessary to see them as seperate things in order to understand the situation.

And here is why NASCAR has no speedoneters , yet they have a speed limit on pit road and are able to attain that with RPMs and gearing. During practice and pace, laps the pace car ( with a speedometer ) will lead everyone down pit lane. Each driver must then learn wich RPMs in which gear equal the speed limit.

You are correct Sensate. Heavy equipment has the speedometer incorporated in the tachometer.

Your friend is correct, assuming the clutch isn’t slipping.

As an alternative my gps posts road speed limit and my speed. It even dings at me when 10 mph over, plus directions.

Barky, that feature would drive me nuts.
Therefore, allow me to speculate that it’ll be mandated on all cars soon…
Heck, in another 15 years it’ll probably automatically print a speeding ticket.

Your friend is absolutely right, You, I would guess are more about “feelings” and less about simple mechanics.

As the others have said the friend is correct. If your Mazda Miata was an automatic you could be correct, but its not. If you see a significant variation in rpm and road speed for a particular gear the only reason would be the clutch is slipping. Now in SF on some very steep hills a slipping clutch isn’t too big a stretch for me.

Now a motor under load will make a different sound at the same rpm as the same motor going downhill in a no load situation. The rpms and speed can be the same but the exhaust noise will be completely different.

As Will Strunk said, "If you don’t know how to pronounce a word, say it loud!"
So thank you all for the lesson!

As to my being a more “feeling” type than my pal, I would agree in the Myers-Briggs sense of the term, but thankfully that doesn’t prevent my learning and appreciating the logic of mechanical engineering. What had thrown me was articulated by Uncle Turbo:

“Now a motor under load will make a different sound at the same rpm as the same motor going downhill in a no load situation. The rpms and speed can be the same but the exhaust noise will be completely different.”

Thanks again!

I’m going against the consensus here because I’ve seen the data. Going up a steep hill requires quite a bit of engine torque, hence the need for first gear. The more torque you apply to the tires, the more they will slip. They won’t spin, or smoke but they will “slip” a bit because the rubber tread is squishy and the drive force will compress the tread when it is in contact with the ground and snap back when it lifts. That slip, on a steep hill will be as much as 5%, causing the tachometer to run 5% HIGH uphill and 5% LOW going down the same hill because gravity causes the force on the tires. The tach will be 95% accurate on the hill and essentially 100% accurate on level ground assuming the clutch is not slipping.

@Mustangman, I disagree with that notion. We are talking about a Miata, not a top-fuel dragster or a trophy truck hill climber. Unless you spin the tires, typical car tires will maintain a static connection to the road with extremely little sidewall flex as you describe. And, any flex would need to continuously increase to maintain a 5% rpm differential. Not happening.

Yeah my Riv had a speed warning buzzer. Finally just set it at 80 and forgot about it.

I agree with BustedKnuckles. A Miata spinning its tires on an upgrade is highly unlikely unless the road surface is wet, icy, or sanded.

@BustedKnuckles “Slip” is not actual sliding or spinning as I mentioned in my post. It is the gain or loss in rotation due to the elastic nature of the tire and the forces applied to it. Click the attached link, scroll down to “Longitudinal Forces”. This explains the effect and shows the braking slip curve in Fig 6.8:

It is under the heading of racing tire technology but titled Tire Behavior. All tires exhibit this. It is a hard thing for even an engineer to wrap their head around but it is real. The effect is fairly linear with applied torque up to about 8 to 12 percent, depending on the tire.

Whether this is a Miata, with little torque, or a Viper, with lots of torque, this effect is present.

For the purposes of this discussion, if that tire slip affects rpms, it will affect the speedometer by the same amount. It won’t be apparent to the average driver. To the cop hiding behind a tree at the bottom of the hill with a radar gun, it’s another matter of course.

I agree with @Mustangman - any time a rolling tire has force applied to it (turning, starting, stopping, or maintaining speed on an uphill or downhill) some slip will occur.

But it’s very small in this situation, as he said, and I’d bet $10 the OP would never notice it. They’re noticing the very different sound of the engine under load and not under load.