Anthony Rhodes wrote:
>
> >Where Dan is wrong though, is that the V8 does provide you with extra power
> >and torque and you will then reach said speed more quickly than in a stock
> >powered car. The quickness is related to acceleration and the quicker you
> >able to accelerate the more force your car is carrying and the more braking
> >force is required to stop it. This is where Dan is mistaken.
>
> Kai, Kai, Kai, what are you thinking? How does the true statement that "
>the quicker you [are]
> able to accelerate the more force your car is carrying" have anything to do
>with STOPPING???
>
> Stopping is stopping and going is going, and ne'er the twain shall meet. The
>only way you need
> more stopping power simply due to more horsepower is if you leave it in gear
>and a foot on the gas
> as you hit the brakes.
I have been somewhat absent from this discussion, due to a sort of
emotional roller coaster ride I've been on in the last few days (waking
Monday morning to find a message telling me that one of the people
working for me, a friend whom I'd known for ten years, had died over the
weekend, ensuing funeral services, wake, etc., my mother going into two
days of cancer surgery on Monday, my daughter's birthday the same day).
But, given all the remarks made, let's keep Dan Masters' original
postulation in perspective. He said, essentially, if there was no change
in the weight of the vehicle, braking power was unaffected. Others said,
in essence, "but, you're going to run the vehicle faster, so more
braking power is necessary," and Kai Radicke said:
> Where Dan is wrong though, is that the V8 does provide you with extra power
> and torque and you will then reach said speed more quickly than in a stock
> powered car. The quickness is related to acceleration and the quicker you
> able to accelerate the more force your car is carrying and the more braking
> force is required to stop it. This is where Dan is mistaken.
Let's try to get back to the basic physics. Dan has said, and let's
assume for the moment, that the weight of the vehicle is unchanged. The
basic formula for force is:
f=ma
where:
f=force
m=mass
a=acceleration
In braking, friction is used to convert kinetic energy to heat. Braking,
by definition, is negative acceleration (deceleration). Kai Radicke's
logic is that because the car accelerates faster, it needs more braking
power. Let's pursue that one a bit further. If we invert the
acceleration formula above for braking, we get:
-f=m(-a)
What the formula above says is that negative force (braking) equals the
negative of the original acceleration force equation. This is what Kai
Radicke asserts, i.e., faster acceleration requires an equal
deceleration force. This assumes that the absolute value of -a must be
equal to a. Sorry, but not true, according to the original postulation
of Dan Masters.
What this inverted formula says is that braking force should equal
acceleration force. Kai asserts that this simple formula is true, that
deceleration force should equal acceleration force. In simpler terms,
what Kai is suggesting, and as the above formula suggests, if a and -a
are the same absolute quantity) is that the _rate_ of deceleration must
be equal the _rate_ of acceleration (let's keep in mind that any formula
involving acceleration or deceleration is rate-dependent). In even
simpler terms, based on the formulae above, this assertion is that if
the car goes from 0 to 60 mph in five seconds, it must also be able to
go from 60 to 0 in five seconds.
That's not what Dan has said, nor is what he has assumed in the
argument.
For the purposes of this argument, if the brakes are physically
unchanged, the friction coefficient and the swept area of the brakes
determine, regardless of potential engine power, the variable -a
(negative acceleration), so the only remaining variable is m (mass). If
mass is unchanged, and is always a positive quantity, then the negative
force (braking power) is unchanged with a fixed -a. Since acceleration
is rate-dependent, negative acceleration (deceleration) is
rate-dependent, as well, and if deceleration begins at 60 mph and ends
at 0 mph, starting speed, ending speed and rate of deceleration (-a,
based on the physical characteristics of the brakes, which are presumed
to be unchanged) then those quantities determine -F=-force. -F, for both
instances (stock and modified) is the same, so the only variable left is
m. Period. Engine power or rate of acceleration has nothing to do with
the deceleration formula.
Suggestions that one might drive the car differently, having more power
available, are irrelevant to the original argument. Such suggests a
change in variables (such as braking from top speeds in excess of the
design limitations of the original brakes, or repeated braking inducing
fade, or suggestions that drum brakes are different in character than
disc brakes, or any other arguments not related to the original
postulation). Those were not part of the original assertion.
All that said, would I, putting a 350 hp engine in a car normally
equipped with a 110 hp engine think that better brakes, given natural
human tendencies to excess, be a good idea? Yes, perhaps. Nevertheless,
that immediately begs new calculations based on behavior, rather than on
physics.
The original remark by Dan was in essence that, all other things being
equal, without a change in mass, without a change in braking power,
deceleration will not change. This is true. If the mass is unchanged,
and braking force is unchanged, then the rate of deceleration is
unchanged. End. Finito. Period. Absolutomente. That's simple physics and
mathematics, based upon the _absolutely_ same formula used to calculate
force on acceleration, which is the basis of the original disputes
asserting required changes in deceleration because more power is
available for acceleration. The mistake of others here has been to
incorrectly assume that rates of deceleration must linearly follow rates
of acceleration.
Argue at your peril. <big smile>
Cheers, all.
--
Michael D. Porter
Roswell, NM (yes, _that_ Roswell)
[mailto:mporter@zianet.com]
`70 GT6+ (being refurbished, slowly)
`72 GT6 Mk. III (organ donor)
`72 GT6 Mk. III (daily driver)
`64 TR4 (awaiting intensive care)
`80 TR7 (3.8 liter Buick-powered)
`86 Nissan 300ZX (the minimal-maintenance road car)
`68 VW Type II Camper (Lancia twin-cam powered, but feeling its age....)
Remember: Math and alcohol do not mix... do not drink and derive.
/// triumphs@autox.team.net mailing list
/// To unsubscribe send a plain text message to majordomo@autox.team.net
/// with nothing in it but
///
/// unsubscribe triumphs
///
|