Engine RPM and Vehicle Speed

Each and every vehicle provide cluster meter which shows different indications along with Engine RPM and Vehicle Speed.In this article,we will try to get the proper connection between these two.

Cluster meter showing Engine RPM and Vehicle Speed

  

There are several meters and indications regarding our vehicle inside that cluster meter. However, we will cover those all indication in another future article, here we discuss about meters fitted inside the cluster.

Generally, there are several meters which are mentioned below,

1. ODO meter (which shows How much Km Vehicle has Run)
2. Speedometer (which shows Current speed of the vehicle)
3. RPM meter (which shows Current RPM of the Engine)
4. Fuel Meter (Which indicates quantity of fuel available in the tank)

We are used to look at our cluster meter hundreds of time in a day and if you have noticed that during accelerating the vehicle, RPM-meter also starts rising along with the speedometer. I hope WHY??? and  How??? are generated in your mind. Let’s try to understand this.

Why RPM meter indicator start increasing along with speedometer during accelaration?

In a technical language,RPM meter shows the RPM generated by engine and this RPMs(Revolutions) are trasmitted to the vehicle tyres through various componants of transmission system and the speed which is shown by the speedometer is calculated with the help of the tyre RPM and it’s diameter.Inshort,Engine RPM,tyre RPM and vehicle speed are leaves of the same branch of a tree and they are in direct proportion.

How the speedometer and RPM meter increase/decrease in same manner?

As I explained earlier,Engine RPM is the source and it magnifies or demagnifies with the help of the gears in gearbox and final drive(Differntial  or axle drive).Now we define the vehicle speed from engine RPM with all calculations.

Derivation of vehicle speed from Engine RPM.

Assumptions (Logically,some of them are perfectly true),

1. There is no play in between each and every gear-mashing
2. Engine RPM is constant and there is no disturbance in rotations
3. Engine RPM=Gearbox Input RPM
4. Gearbox Output RPM=Differntial Input RPM
5. Differntial Output RPM=Tyre RPM

Suppose,

Engine RPM=3000     ……….……….……….……….……….……….……….……….……….……….……….……….……….……….………….……….……….…….(1)

Gearbox Specifications =1^st Gear (Gear Ratio=3.58),2^nd Gear (GR=1.93),3^rd Gear(GR=1.28),4^th Gear(GR=0.76)     ……….……….……….……….….……….(2)

Final Drive(Differential) Gear Ratio=3.82        ……….……….……….……….……….……….……….……….……….……….……….……….……….…….….………(3)

Tyre outer Diameter=30 inches        ……….……….……….……….……….……….……….……….……….……….……….……….……….…….………….…………(4)

Now,First of all we have to know about gear ratio.

Driving And Driven Gears

It can be stated as,

Gear Ratio=(Input RPM/Output RPM)=(No. of teeth of output gear/No. of teeth of input gear)     ……….……….……….……….….……….……….…………….(5)

We know that,

There are main two Gear Ratios in driveline and they are: Transmission Gear Ratio (Gearbox GR), Final Drive Gear Ratio (Differential GR)

According to [eqⁿ…..….(5)],

Transmission Gear Ratio=(GB input RPM/GB output RPM)     ……….……….……….……….….……….……….……….……….……………….……….……….(6)

&

Final Drive Gear Ratio=(Differential Input RPM/Differntial outut RPM)     ………….……….……….……….….……….…………….……….……………….…….(7)

Now,

Overall Gear Ratio= TGR x FDGR

=(GB input RPM/GB output RPM) x (Differential Input RPM/Differntial output RPM)

[From eqⁿ(6) & eqⁿ(7)]

=(GB input RPM/Differntial output RPM)

[From Assumption 4]

=(Engine RPM/Tyre RPM)

[From Assumption 3 & 5]

• Overall GR=(TGR x FDGR)=(Engine RPM/Tyre RPM)   
• Tyre RPM=[ (TGR x FDGR)/Engine RPM ]
• Tyre RPM = [ 3000/(TGR x 3.82) ]     ……….…[From eqⁿ(1) & eqⁿ(3)]…….……….……….….……….…………….……….…………….…….……….(8)

Now, we all know that,

Velocity=Distance/Time

=(No. of Tyre Revolutions)x(Tyre Outer Diameter)/Time for these Revolutions

=Tyre RPM x Tyre Diameter _{(inch/minute)}                                                     [RPM=Revolution/Minute]

= Tyre RPM x 60  x 30 x 0.0000254 _(km/h)

• Vehicle Speed = Tyre RPM x 30 x 25.4 x 60 _(km/h)      .…………….……….……………….……….……….…………….……….…….…….….……….(9)

Now from Eqⁿ (2),(8) & (9),

Gear	TGR	Tyre RPM	Vehicle Speed(km/h)
		3000/(TGR x 3.82)	Tyre RPM x 60  x 30 x 0.0000254
1st	3.58	219.3688	100.2954
2nd	1.93	406.9121	186.0402
3rd	1.28	613.5471	280.5137
4th	0.76	1033.343	472.4442

If Engine’s maximum RPM is 3000 then these speeds are the maximum for different gears respectively. This vehicle speed is showed according to its No. of gear to the Speedo meter.It is totally depend upon throttling process or given accelerator.Even at the maximum gear the engine would not reach at its maximum capacity of 3000 RPM untill the full throttle will be given.

[Note:-Here one thing should be noted that we considered constant engine speed so we get constant speed for specific gear but actually when we accelerate or decelerate, the engine RPM gradually changes and along with that the vehicle speed will also gradually change in direct proportion.]

We are glad to inform you all (Readers) to comment down if there are any confusions or there are several mistakes (Overall,we are still humans).

Thank you very much for your precious time.

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