OK, so here's one for you...

If I put my car into top gear and set the engine to 3,500 revolutions 
per minute, my car travels forward at almost exactly 75 miles per hour. 
So... how far forward does it travel for a single revolution of the engine??

Similarly, at that speed my car achieves roughly 50 miles per gallon of 
fuel. So how much fuel does it inject into each cylinder??

[My car has a four-cylinder, four-stroke internal compustion engine, and 
is normally-asperated. And runs on petrol, in case that wasn't obvious. 
Presumably the timing is therefore set so that exactly one cylinder 
fires for every revolution of the engine.]

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

Post a reply to this message

Invisible wrote:
> OK, so here's one for you...
> 
> If I put my car into top gear and set the engine to 3,500 revolutions
> per minute, my car travels forward at almost exactly 75 miles per hour.
> So... how far forward does it travel for a single revolution of the
> engine??
> 
> Similarly, at that speed my car achieves roughly 50 miles per gallon of
> fuel. So how much fuel does it inject into each cylinder??
> 
> [My car has a four-cylinder, four-stroke internal compustion engine, and
> is normally-asperated. And runs on petrol, in case that wasn't obvious.
> Presumably the timing is therefore set so that exactly one cylinder
> fires for every revolution of the engine.]
> 
Nope. Each cylinder fires once for every two revolutions. You have a 4
cyl engine therefore two cylinders fire for each rev.

John

-- 
I will be brief but not nearly so brief as Salvador Dali, who gave the
world's shortest speech. He said, "I will be so brief I am already
finished," then he sat down.

Post a reply to this message

Invisible wrote:
> OK, so here's one for you...
> 
> If I put my car into top gear and set the engine to 3,500 revolutions 
> per minute, my car travels forward at almost exactly 75 miles per hour. 
> So... how far forward does it travel for a single revolution of the 
> engine??

574643.


the "almost" you told, neither tires wearing nor possible sliding.

> Similarly, at that speed my car achieves roughly 50 miles per gallon of 
> fuel. So how much fuel does it inject into each cylinder??

None.

> [My car has a four-cylinder, four-stroke internal compustion engine, and 
> is normally-asperated. And runs on petrol, in case that wasn't obvious. 
> Presumably the timing is therefore set so that exactly one cylinder 
> fires for every revolution of the engine.]

-- 
Eero "Aero" Ahonen
    http://www.zbxt.net
       aer### [at] removethiszbxtnetinvalid

Post a reply to this message

On Fri, 16 May 2008 20:40:04 +0300, Eero Ahonen wrote:

> Ah, you want the unit? µm, naturally. This of course doesn't take count
> the "almost" you told, neither tires wearing nor possible sliding.

Or the effects of momentum. ;-)

Jim

Post a reply to this message

Invisible <voi### [at] devnull> wrote:
> OK, so here's one for you...
>
> If I put my car into top gear and set the engine to 3,500 revolutions
> per minute, my car travels forward at almost exactly 75 miles per hour.
> So... how far forward does it travel for a single revolution of the engine??

Is this a math puzzle, or a real question?

If it's a real question, it's almost impossible to answer from the information
given.  You have to take into account acceleration, momentum, friction, etc.

....Chambers

Post a reply to this message

>> If I put my car into top gear and set the engine to 3,500 revolutions
>> per minute, my car travels forward at almost exactly 75 miles per hour.
>> So... how far forward does it travel for a single revolution of the engine??
> 
> Is this a math puzzle, or a real question?
> 
> If it's a real question, it's almost impossible to answer from the information
> given.  You have to take into account acceleration, momentum, friction, etc.

How so?

The engine is directly coupled to the wheels. Unless the car looses 
traction, the forward motion of the car and the rotational speed of the 
wheels and engine all have a simple linear relationship.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

Post a reply to this message

On Fri, 16 May 2008 21:11:34 +0100, Orchid XP v8 wrote:

>>> If I put my car into top gear and set the engine to 3,500 revolutions
>>> per minute, my car travels forward at almost exactly 75 miles per
>>> hour. So... how far forward does it travel for a single revolution of
>>> the engine??
>> 
>> Is this a math puzzle, or a real question?
>> 
>> If it's a real question, it's almost impossible to answer from the
>> information given.  You have to take into account acceleration,
>> momentum, friction, etc.
> 
> How so?
> 
> The engine is directly coupled to the wheels. Unless the car looses
> traction, the forward motion of the car and the rotational speed of the
> wheels and engine all have a simple linear relationship.

There isn't a linear relationship between the rotational speed of the 
wheels and the speed of the engine.

If I take my foot off the gas, the engine revs drop.  The car may or may 
not slow down (depending on the road and the landscape).

Similarly, if I apply the brakes to a full stop, the engine doesn't die, 
it idles.

Then of course if you put the car in neutral, you've completely 
disengaged the engine from the wheels.

Jim

Post a reply to this message

Invisible <voi### [at] devnull> wrote:
> If I put my car into top gear and set the engine to 3,500 revolutions 
> per minute, my car travels forward at almost exactly 75 miles per hour. 
> So... how far forward does it travel for a single revolution of the engine??

  Isn't this laughably simple to calculate?

  3500 rpm = 3500*60 rph, and in 1 hour it travels 75 miles. Thus divide
75 miles by 3500*60 revolutions, and you have the amount of miles per one
revolution, which would be approximately 0.0003571428 miles.

  Given that I'm not sure which whacky units miles are divided into,
I'll just convert those to more understandable units, so 75/(3500*60)
miles is approximately 57.5 centimeters.

-- 
                                                          - Warp

Post a reply to this message

Jim Henderson wrote:

> There isn't a linear relationship between the rotational speed of the 
> wheels and the speed of the engine.

Well that's news.

> If I take my foot off the gas, the engine revs drop.  The car may or may 
> not slow down (depending on the road and the landscape).

Not true. The engine revs depend on the speed of the vehicle.

If you don't believe me, try rolling down a hill at 30, and then stick 
the car into 1st gear. Watch the revs go through the roof, even though 
you haven't touched the gas.

> Similarly, if I apply the brakes to a full stop, the engine doesn't die, 
> it idles.

Um, yes it does. Unless...

> Then of course if you put the car in neutral, you've completely 
> disengaged the engine from the wheels.

...you disenguage the engine from the wheels. Then there really isn't 
any relationship. But as long as the car stays in the same gear, there 
is a fixed relationship.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

Post a reply to this message

>> If I put my car into top gear and set the engine to 3,500 revolutions 
>> per minute, my car travels forward at almost exactly 75 miles per hour. 
>> So... how far forward does it travel for a single revolution of the engine??
> 
>   Isn't this laughably simple to calculate?

Yes - *if* you can do things like compute 60/75 *mentally*. :-P And also 
if you know how many yards there are in a mile, and all kinds of other 
random stuff.

[I found myself wondering about this in the car on the way home.]

Now, if you have access to a *computer* - or even better, Google - then 
yes, it becomes quite easy.

>   Given that I'm not sure which whacky units miles are divided into,
> I'll just convert those to more understandable units, so 75/(3500*60)
> miles is approximately 57.5 centimeters.

That's the number I arrived at too.

Google also tells me that 75 mph = 33 m/s. Which frankly seems really 
damned fast. (!) I mean, my car is only, like, 4 m long or something... 
That means the car covers almost 10x its own length in 1 second! o_O

No wonder hitting anything is an instant fatality...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

Post a reply to this message