Engine RPM vs Cruising Speeds Part 1

Preamble
Early in October this year, I’d essayed on the fuel ‘efficiency’ vs fuel ‘consumption’ of a car, giving an example of an old Zen cruising at different speeds.

As a fallout of it, a friend posed me some further questions but this time, talking about the differences in engine rpm as displayed by the Tacho on Dash for different cars. This is how the QnA went…

Question
I was reading the other day an AutoExpress/UK review about a BMW-5 Series which does 100 mph @ 1700 rpm. My question to you is how do these guys make an engine perform at such low rpm’s at such high speeds, considering that my Verna-D though not comparable to the BMW, touches 100 kph only at around 2200 rpm in 5th.

So is there a specific logic to their engine/gearbox design that such cars work leisurely at much lower rpm’s whereas the rest are really pulling more than twice that number. I am foxed and hence this question to you. CM/Hyd.

Answer
Thanks for the teaser CM. After a long time some one has asked me an interesting question that sends my creative juices a-flow. Coming down to think of it, it’s not much of a brainer. So here we go:

We all know that an ICE basically produces a ‘torque’ i.e. a ‘rotary force’, like an electric motor and, therefore, has an Rpm vs Torque ‘Characteristic’. We also know that ‘torque’ is primarily responsible for the accelerating ‘capability’ of a car, of course in tandem with its gearbox/ratios.

Since ‘power/(b)hp’ i.e. ‘rate of doing work’ is a direct multiple of torque and rpm, it follows that - a) the bhp vs rpm ‘characteristic’ of an ICE closely follows the shape of its primary torque vs rpm characteristic and, b) that the ‘max power’ dictates the top-speed ‘capability’ of a car.

Now, the power required to move a car at ‘a’ speed basically depends on - a) its ‘road-rolling resistance’ and, b) the ‘wind resistance’ faced by it. At higher speeds, the latter is predominant and it goes up ‘exponentially’ with road speed.

Coming now to the root of your question. Assume for a moment that (a)+(b) above are the same for a Verna-D and a BMW-5D, for a road speed of 100 mph/160 kph, that a Verna is also quite capable of doing, AND that to move them at this speed, their respective engines must produce the same, say, 100 bhp.

Now comes the crux. Since the Verna can do only ~110 bhp/max, say at 4,000 rpm, to be doing 100 bhp for a 160 Kph speed, it’s engine will have to be spinning at least at 4000×100/110 = 3636 rpm.

On the other hand, the BMW-5 produces 190 bhp at 4,000 rpm. Therefore, for it to produce only 100 bhp to move @ 160 Kph, its engine stands run only at 4000×100/190 = 2105 rpm, or 58% of what the Verna has to do. And eureka, this is more or less what you’ve observed!

Please note that the actual bhp vs rpm figs in real life will vary, depending upon the ’shape’ of their individual bhp/rpm curves but for simplicity’s sake, I’ve taken them to be a straight line @ 45*.

Moral of the story, a high/max bhp engine doesn’t mean it can rocket a car to the moon BUT the ‘reserve’ power it has while cruising at an optimum or recommended road speed, so that - a) it cruises with the engine most ‘relaxed’ and more importantly, b) it has a tiger-in-waiting to literally ‘leap forward’ as and when required - either for over taking or just for the kicks!

It’s with this funda at the back that some of the current models of Rolls’ don’t have a conventional/rpm Tacho on the Dash. Instead, what they have is an rpm meter ‘calibrated’ in terms of ‘remaining’ engine power at a given rpm, showing ‘Percentage Reserve Power’ at any driving speed in any gear!

And coming down to think of it, not so long ago until the world at large started laying due or undue emphasis on max torque and max bhp even for high end cars as their USPs, ‘RR’ used to declare ‘Adequate’ against the Engine/bhp columns of its Specs!!