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RPM versus MPH

Old Apr 10, 2004 | 09:57 PM
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RPM versus MPH

An interesting conversation cropped up on https://www.rx8club.com/showthread.p...threadid=25338 and using the following information on the UK Website I went ahead and got the following numbers for our 6-speed and automatic models.

The above figures are based on stated Gear Ratios and information from HERE and Miata.net website that it takes 777.0 turns of the 225/45R18 Tires to travel one mile.

The numbers come close to real-life but I see a few MPH drop beginning at 3-4K due to drag. The numbers drop significantly as the car moves faster and drag builds up.

BASIS FOR CALCULATIONS:

As an example, for third gear on the 6 speed box, the Gear Ratio of 1.65 means that for each FULL revolution of the crank shaft (not rotor) there will be 1.65 times FEWER revolutions within the Gear Box. The 'Final Gear Ratio' then means that there will be 4.444 times FEWER revolutions of the Prop Shaft (and hence of the rear wheels). For 4000 rpm (and taking into account the conversion from minutes to hours), this gives an equation as follows:

Speed = (4000 x 60)/(1.65 x 4.444 x 777.0)

= 42.16 mph
Attached Thumbnails RPM versus MPH-rpm_mph.jpg  

Last edited by brothervoodoo; Oct 14, 2004 at 05:47 PM.
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Old Apr 11, 2004 | 06:18 AM
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Nice Math

Has anyone attempted Max Speed on their RX. I've not had mine over 100 but we don't have a lot of straight/open roads here in S. MD. Thought maybe some of the RX owners out West may have tried it on some of those long straight highways?
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Old Apr 11, 2004 | 09:40 AM
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i actually had mine uo 125 screwing around with this guy on the interstate late one night....not sure what the RPM's were...but i am pretty sure i was in 4th gear to keep the RPM's up at the throttle response high
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Old Apr 11, 2004 | 11:34 AM
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In the U.S. we're electronically limited to 149 MPH. Not sure about other countries.
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Old Apr 11, 2004 | 12:43 PM
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I have some problems with Brothervoodoo's figures.

First, to dispose of a detail, the auto second gear in Mazda's book, p. 49, is 1.543, which doesn't round to 1.55.

What's important is to take a "stock wheel" number from a Miata site and use if for a particular tire on the RX8. The result is to get figures considerably different than reported in respected sources. To be specirfic, Road & Track says the RX8 turns 3,100 revs at 60 in 6th. Do the math (60 divided by 3.1 thousand) and you get 19.4 mph per 1,000 rev. I have seen a 20 mph figure in other mags, but never more.

I don't put 100% trust in any figure, because there are different versions, but I have a lot more confidence in Road & Track'stechnical ability, applied to the exact car, than in some generic table.
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Old Apr 11, 2004 | 01:07 PM
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I linked and quoted the sources I found, the numbers can be reworked. "URL" me to some better sources and it can be re-computed in Excel in less than 10 seconds.
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Old Apr 11, 2004 | 02:52 PM
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all it is is speed=rpm/gear ratio/final drive ratio/tire circumfrence
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Old Apr 11, 2004 | 04:13 PM
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pretty cool man...
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Old Apr 11, 2004 | 06:01 PM
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Re: RPM versus MPH

Originally posted by brothervoodoo
The numbers come close to real-life but I see a few MPH drop beginning at 3-4K due to drag. The numbers drop significantly as the car moves faster and drag builds up.
Why does drag have any effect on speed in gears? The gears and wheels go 'round no matter what the drag at any particular speed don't they?

Otherwise, nice writeup.
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Old Apr 11, 2004 | 07:35 PM
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Re: Re: RPM versus MPH

Originally posted by Spin9k
Why does drag have any effect on speed in gears? The gears and wheels go 'round no matter what the drag at any particular speed don't they?
If the back wheels are just "spinning" with no forward movement or if you drove in outerspace where no friction is involved, they would put down the "speed" indicated on the chart. In real life, as you move forward, you have to push the wind out of the way and that resistance slows you down. If you had a 100mph headwind you would go slower still at any specific RPM range.

If anybody can offer and point me to some better data regarding the gear ratios, or how many revolutions the stock tires make in a mile, let me know. I don't see how using the rotation formula from the miata link is contradictory. If you look at the second half of that page they are doing basic calculations for any tire size which has nothing to do with the miata.
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Old Apr 11, 2004 | 07:54 PM
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Re: Re: Re: RPM versus MPH

Originally posted by brothervoodoo
If the back wheels are just "spinning" with no forward movement or if you drove in outerspace where no friction is involved, they would put down the "speed" indicated on the chart. In real life, as you move forward, you have to push the wind out of the way and that resistance slows you down. >>>>If you had a 100mph headwind you would go slower still at any specific RPM range. <<<<<
Sure the air resistance slows THE WHOLE CAR down, but an engine is DIRECTLY connected to the transmission, which is DIRECTLY connected to the wheels, which is DIRECTLY connected to the road surface. UNLESS there is SLIPAGE of the tires ON THE ROAD, the RPMs are STILL contstant at any speed - regardless of air resistance!

IOW Unless the TIRES ****slip**** on the road at speed then the engine RPM is constant (at any particular speed) wheather you are on the moon (no air friction) or on earth (w/air resistance).

I am either totally missing your point (on this one subject) or I don't understand how it is possible to misunderstand this. Sorry but I think you are not correct here - certainly no offense - I just being logical (I believe).

Last edited by Spin9k; Apr 11, 2004 at 08:28 PM.
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Old Apr 12, 2004 | 03:47 PM
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The tyres deform under load (increases with speed -> drag force) so the effective radius becomes smaller than the theorythical at high speeds.

I'm not sure about the scale of this but could account for a few mph around top speed.
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Old Apr 12, 2004 | 05:12 PM
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speed and rpms are mechanically linked together for each gear... end of story, its cut and dry, no buts, no exceptions, no excuses...
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Old Apr 12, 2004 | 05:36 PM
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Sure you are right is we consider the instrument readouts!

I was thinking about real speed (GPS) vs RPM.

Tamas
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Old Apr 13, 2004 | 09:57 PM
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Anyone know the coefficient of drag for the 8?
My real world #'s are (4AT):

1st: 45mph
2nd: 80mph
3rd: 120-122mph didn't see the exact #
4th: dunno, don't want to pay that ticket, but i do know that even if 189 mph were possible, it would take a week to get there :D
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Old Apr 13, 2004 | 10:18 PM
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Originally posted by therm8
Anyone know the coefficient of drag for the 8?
My real world #'s are (4AT):

1st: 45mph
2nd: 80mph
3rd: 120-122mph didn't see the exact #
4th: dunno, don't want to pay that ticket, but i do know that even if 189 mph were possible, it would take a week to get there :D
To get to those speeds on the auto you were using the paddle shifters, correct? The formula does seem to pan out and/or come close.
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Old Apr 14, 2004 | 04:11 PM
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there would be slippage in the torque converter, unless it has a lockup ... i've really read nothing about the automatic on the 8.

so the automatic #'s wouldn't pan out the same way as the manual numbers
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Old Apr 14, 2004 | 06:48 PM
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all automatics since the 80's have a lock-up torque converter...


Drag is a force, it effects acceleration. It acts in the direction opposite the direction you travel. It has no impact on RPM vs MPH. If your car goes 120mph in 4th gear at 7,000 rpms, its will always be going at 120mph at 7,000 rpms in the real world or a dragless world as long as your wheels are not spinning. Its a mechanical interlock.
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Old Apr 14, 2004 | 08:47 PM
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So then the chart formula must be flawed because I don't see a correlation when in upper revs (say above 4-5K) the numbers just don't match up. They do at lower revs though.
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Old Apr 15, 2004 | 06:11 PM
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i believe bridgestone lists the re40's as 780 revolutions per mile... try that
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Old Apr 21, 2004 | 01:38 AM
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1st - 40
2nd - 65
3rd -90
4th - ive only been to 110
5th
6th
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Old Apr 21, 2004 | 11:57 PM
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It'll gitty up to 130+ in 6th without much difficulty. Obviously lower gears are easier.
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Old Apr 22, 2004 | 06:30 PM
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I have to agree with Spin9K and Pr0ber - RPM vs MPH is the same whether you are driving in hurricane gale force tail winds or not. MPG, max MPH and numerous other abreviations would definitely be effected though.

Did get mine over 105 easily on a recent roadtrip - I think I need some countermeasures though before trying for max speed.

I thought it handled well at the higher speeds - felt pretty comfortable.

Man this is a great car.
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Old Apr 22, 2004 | 07:36 PM
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Re: RPM versus MPH

Originally posted by brothervoodoo
...means that for each FULL revolution of the crank shaft (not rotor) there will be 1.65 times FEWER revolutions within the Gear Box...
Ok, this is something that's been driving me crazy.... I understand that the crankshaft turns 3 times for each revolution of the rotor. That being said, what does the tach measure? If it's the crankshaft speed, that means that the rotors are turning 1/3 as fast as the speed reported on the tach. Therefore, the maximum engine speed is 3k RPM's of the rotors. In a piston engine, I thought RPM's were defined as how many complete piston cycles occur in one minute, which I believe happens to be the same number as how many crankshaft turns occur in one minute (one cycle of the pistons = one revolution of the crankshaft). This means that at 9k RPM's, your pistons are cycling 9k times in one minute, but on a rotary, 9k RPM's only means 3k rotor turns per minute. On the other hand, if the rotors spin at 9k RPM's, that means the crankshaft spins at 27k, which seems a little ridiculous to me. Bottom line here: How fast do the rotors spin? 9k or 3k?
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Old Apr 22, 2004 | 09:36 PM
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3k
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