HELLO EVERYONE AND WELCOME
in this video we're gonna be talking about
when to shift gears in order to maximise accerleration
and so here we what we are doing is
our goal is to maximise the force of
the driven wheels on the ground
across any speed, any rpm whatever gear
force to be as large as possible as
we're accelerating so here we have a
beautiful blue Honda S2000 that was very
obvious just from looking at the sketch
and so we're trying to maximize this
force here now two of the assumptions
that we're going to make we're going to
assume that we have infinite tractions
we don't have to worry about that as far
as gearing is concerned and we're also
going to be assuming we're driving in a
straight line so there could be tracks
where for example you're going around a
corner and it may not be beneficial to
upshift and then downshift again may be
beneficial just leave it in gear or
going to ignore that we're just going in
a straight line we want to know when is
the best time to shift gears based on
our p.m. and you're gearing so in order
to maximize this force at the wheels we
want our torque at the wheels obviously
to be as large as possible so your
engine sends torque back it goes through
the transmission hits the rear
differential comes to your wheels you
want that torque at the wheels to be as
large as possible that torque at the
wheels is equal to the force that it's
applying multiplied by the radius of
that tire so now that we're kind of
changing this from our goal is to
maximize wheel force we're going to
change that goal to maximizing wheel
torque because they're going to
accomplish the same thing we'll get
maximum acceleration when we have
maximum wheel torque which gives us our
maximum wheel for us so we need to know
what is the equation for the torque at
the wheels within the equation for the
torque at the wheels we have our engine
torque we're going to multiply that by
the gear ratio of whatever gear we are
in we're going to multiply that by our
final drive ratio and that could also be
multiplied by other gear reductions for
example in the hon s2000 there is
another gear reduction in the
transmission before it gets to the final
drive and then you will of course
multiply that by any losses that you
have through the transmission now the
losses will of course apply to every
gear and the final drive ratio and the
gear reduction are constant so we're
just going to ignore these because these
aren't really going to change with each
gear our variables here are the engine
torque which of course depends on our
p.m. and our gear ratio which just
depends on which gear you put it in so
we're going to see max
engine torque with the throttle wide
open so moving on we want to maximize
this number right here multiplied
together engine torque x gear ratio we
want that as big as possible always and
that's going to give us our highest
wheel torque so looking at the Honda
s2000 gear ratios here I have them one
through six it's a 6-speed manual
transmission and so our gears here we
have so for example 3.1 33 in first gear
versus 2.0 45 in second gear so what
that means if you take 3.1 3 3 and
divide it by 2 point 0 4 5 there's a
fifty three percent difference there so
you're going to have fifty three percent
more wheel torque in first gear at the
same engine rpm as you would in second
gear what that of course the drawback to
that is you don't have as high of a top
speed so second gear will go to a higher
speed with less wheel torque first year
will go to a lower speed with more wheel
torque so in order for this in order for
you to need to shift the torque from the
engine has to drop let's say we're going
from first to second gear the torque
from the engine would have to drop fifty
three percent in order for that to be
worthwhile which is going to be very
rare as you might imagine so you're
pretty much going to run that out to
redline so let's look now at a dyno
curve so we can now get the exact
numbers and no you know what should we
do when should we shift gears depending
on which gear ship we're on so this I
just googled Honda s2000 ideally you
would want to die know your vehicle
which I will do eventually but ideally
you're going to want to die know your
vehicle that way you can get the exact
numbers but you can just google it get
something very close I googled s2000
dyno sheet this is a 2002 and it was a
stock vehicle so very close to what I
might find on my own basically what
you've got nice flat torque curve up
until about 6000 rpm then vtech changes
it to a different cam profile and you
get to a higher you know about 130 pound
feet here and then of course as you get
to the higher rpms that power starts to
taper off and so basically what we're
going to look at is is this tapering off
of the torque when should we shift in
this tapering in order to get back into
this peak torque so our
example we're going to be in third gear
we're going to go on flat out and we're
going to want to know you know should we
have shifted at eighty eight hundred rpm
which is red line so we're going to
shift the 8800 rpm and then we're going
to do the math and decide whether or not
that was a good idea so in third gear we
have a gear ratio of 1.4 81 and fourth
year when we shift we have a gear ratio
1.16 one so we're at eighty eight
hundred rpm and third we want to figure
out what RPM that will be and forth so
we just do this simple ratio multiply
8800 by one point one six one divide
that by 1.4 81 and that gives us about
6,900 our p.m. okay so now what we want
to find out is what is the wheel torque
in each one of these gears at this exact
moment so in third gear when we're at
eighty eight hundred rpm you can see
we're making 110 pound feet so 1.48 one
which is our gear ratio x the engine
torque which is 110 10 pound feet gives
us 163 pound feet now in fourth gear
with gear ratio of one point one six one
we are going to be at 6,900 RPM so
that's going to be somewhere in this
range right here as you can see that's
going to be about 130 pound feet so
we'll put in 130 pound feet right there
multiply that across and that gives us
about 150 one pound feet so as you can
see 163 is higher than 151 so what that
means is in third gear at eighty eight
hundred rpm we were putting down more
wheel torque than when we shift down to
fourth even though we're now at peak
engine rpm because of the gear reduction
we're putting down less torque at the
wheels so it was a smart decision to
shift at redline now the idea of
shifting at redline is actually going to
apply to every single gear in my honda
s2000 so if you look at 130 and you
divide that by 110 so that's our peak
that's this nice flat area you divide
that by 110 that gives us about eighteen
percent difference and as you can see
from each one of these gears here
eighteen percent is less of a gear
reduction or a torque disadvantage than
changing gears in any of these so what
that means is basically run it out to
red line and then shift gears and that's
going to be the case for you know tons
of you
out there especially for your initial
gears one through three where there's a
bigger split between the gear ratios you
know it could get different once you get
down into these but basically for most
cars out there it's going to be the case
where you're going to want to just run
it right out to redline you can do the
math yourself and kind of figure it out
but for most vehicles out there because
of the gearing advantage of the lower
gears it's going to be beneficial even
if torque starts to fall off to stay in
that lower gear until you do actually
hit red line and then shift gears and
get back into that peak engine torque
but less wheel torque now a great
resource this book physics for gearheads
I will include a link in the video
description I've mentioned this before
it is a really cool book if you're into
this kind of thing they do a very
similar problem with the Corvette that
used a bit different methodology but
anyways they did the same thing and they
found also that even for this Corvette
zo6 2008 you want to go to red line
every single time gears one through five
before shifting and in order to get
maximum acceleration so it generally
will be the case that you'll just pretty
much go out to redline so when would it
not be ideal to shift at redline well
basically it would be when this number
right here is equal for each gear so
let's say you were in third gear at
8,500 rpm and we're in the s2000 we're
making 102 pound-feet well at that point
it's about equal to being in fourth gear
with a gear reduction with 130 pound
feet now this is less than we have here
but this makes the example work so if
you were at 8,500 rpm and this was your
wheel torque or your engine torque
rather what you want to know is that you
know if you keep going past that your
engine torque goes down and as a result
you're going to be putting less wheel
torque down than if you were to shift
into fourth so this doesn't happen in my
car but it is the case where you know it
would be ideal to shift before red line
if something like this happened and you
were going for maximum acceleration so
thank you guys for watching and if you
have any questions or comments feel free
to leave them below