Security: Implementing A Secure And Usable Internet Password Scheme

When I bought my first real car I became (for the first time) moderately
curious about vehicle performance. I set about to see how it compared to my
previous car performance-wise and was immediately struck by a pivotal
question:

What is the most important attribute for acceleration—horsepower or torque?

My first approach was to ask those immediately around me and call some
friends that were into cars and/or racing. The results were not
satisfactory. I got a few decent responses, but nobody could explain the
relationship to me in a way that I could understand.

Most people have strong opinions on this topic, but no actual grasp of the
science.

All this did was confuse and intrigue me. One thing I did figure out is that
none of the people arguing were using hard science as the foundation for
their argument; they were invoking science, but were doing so very
sloppily. Well, that wasn’t enough for me so I set out to find the real
answers.

The fundamentals

So to start with I naturally consulted
Google. Most of the top hits for “torque vs. horsepower” are excellent pieces;
they break down the math in a very methodical way, so I won’t repeat that
excellent work here. Instead, I’ll just summarize the basics that are
accepted as fact by everyone.

1. Horsepower:
   James Watt
   came up with the concept of
   horsepower
   — which is a measure of, interestingly enough, power. 1 HP is the
   equivalent of 33,000 ft/lbfs per minute. The reason for the complex unit
   is that we’re accounting for three things with this number: the amount
   of weight involved, the distance it’s being moved, and how long
   it takes to do it (that last one is important).

2. Torque:
   Torque
   is nothing more than a measurement of twisting, or rotational,
   force. The easiest way to think of this is to imagine a long shaft —
   like a car’s axle — and imagine it’s in a room suspended in mid air.
   Hanging on the bottom of one end is a rope with a weight attached — a
   very heavy weight.

Now imagine someone trying to, using their hands, twist the shaft so as to
lift the weight. Think of them as essentially trying to act like a winch and
reel it up.

Notice this doesn’t say anything about how fast you’re twisting.

The amount of force they are able to generate by twisting is the torque that
they’re able to produce.

foot-pound

Stop thinking of horsepower and torque as completely separate

Why HP and Torque cross at 5252 RPMs

The mistake most people make when engaging in this debate is considering
horsepower and torque independently. Almost everyone argues as if they are
separate, unrelated values—which they are not.

This equation is the second most important thing on this page, and it’s the
reason that anyone telling you that horsepower and torque should be
considered equally and separately is significantly mistaken. Horsepower is
the product of torque and another value—(RPMs divided by 5252). It’s not
unrelated, separate, or different.

In fact, there’s not a single machine in existence that measures a car’s
horsepower. It’s a man-made number. When a car’s performance is tested, its
torque is measured using a dynamometer.

The measure of an engine’s performance is torque. Horsepower is an
additional number that’s attained by multiplying the torque by the RPMs.

The physics of acceleration

So now for the most important thing on the page. What determines true
acceleration for a vehicle isn’t at all debatable—it’s
force divided by mass. The formula for acceleration is seen below.

f = ma

Which means…

a = f/m

The confusion only comes in determining
which force we’re actually talking about.

So we are solving for acceleration and we have a constant mass. We’ve
already established that torque is the amount of rotational force being
generated at the engine, but
we aren’t concerned with the force at the engine.

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What we’re interested in is the force at the wheels.

The radius of the wheel matters some as well.

The force at the wheels is the f in f = ma.

But remember, the transmission ultimately gives the force to the
wheels, not the engine. And that’s the trick to this whole mess!

Gearing is the translator between the engine and the wheels

So that’s where gearing comes in—it’s the magnifier for acceleration, given
what the engine can produce in power.

Gearing magnifies torque, which is why it’s so important in racing.

This is why the fastest racecars work at extremely high RPMs.

The torque at the wheels is the torque at the engine combined with the
torque magnification given by the transmission through gearing. So the
transmission only sees what’s coming off the engine, while the wheels see
the resulting force combination of the engine plus the transmission.

That’s what horsepower represents! It’s the combination of the benefits of
the engine’s raw abilities combined with RPMs. And RPMs are what allow us to
use gearing effectively, which gives us more torque at the wheels.

And torque at the wheels is the f in f=ma.

Conclusion

So a technical answer to the question of, “What makes acceleration: torque
or horsepower?”, is torque.

But torque at the wheels—not at the engine.

And becauase acceleration is torque at the wheels, the real answer is
horsepower, because horsepower encompasses
not only the engine’s torque but the total torque that gets delivered
to the wheels.

Notes

1. May 7, 2019 — Updated for readibility (typography and formatting), as
   well as writing clarity.

2. Electric engines produce massive torque, which is what makes cars like
   the Tesla so fast.

3. For any comments, corrections, flames, or other types of input, feel
   free to contact me. I’m game for anything that’ll help me better
   understand this interesting subject.

4. Gearing is extremely important because it controls RPMs (and
   therefore horsepower).

5. Gears magnify torque
   — hence the acceleration available in first gear.

6. Another way to validate that it’s power and not torque that matters most
   for acceleration is to look at the cars that have the highest
   acceleration, which are the F1 cars. And guess what? Low torque, high
   horsepower.

7. Another excellent explanation of the topics at allpar.com

8. Another way to see the importance of gearing is to notice how fast some
   low-end cars are able to accelerate in first gear. They feel pretty fast
   at first because they can jump off the line, but it’s really just a
   super high gear that sends lots of torque to the wheels. But it runs out
   quickly.

9. Racecars have high horsepower due to high RPMs, not due to high torque
   (see gearing).

10. “Below 5252 RPMs any engine’s torque will always be higher than its
    horsepower, and above 5252 RPMs any engine’s horsepower will always be
    higher than its torque. At 5252 RPMs the horsepower and torque
    will be exactly the same.” —
    revsearch.com

11. “It is better to make torque at high rpm than at low rpm, because you
    can take advantage of gearing.” —
    vettenet.org