Know You Know: Should We Have Shifted at 88,800 RPM?

In this article, we'll explore the concept of shifting gears to optimize performance and efficiency in your vehicle. Specifically, we'll discuss whether shifting at redline (i.e., the maximum engine speed) is beneficial or not.

We know you know that shifting at 80,800 RPM is a good idea because it's the redline for most engines, including our own. However, to confirm this, let's do some math and see what happens when we shift gears at this speed. When in third gear, with a gear ratio of 1.4:81, we're making 88,800 RPM. If we multiply this by the gear ratio, we get approximately 6,900 RPM. In fourth gear, with a gear ratio of 1.16:1, we're also at around 6,900 RPM.

Now that we know our engine speed when shifting gears, let's calculate the wheel torque in each gear. When in third gear, we're making 88,800 RPM and producing 110 pound-feet of torque. Using our gear ratio (1.48), we can multiply this by the engine torque to get approximately 163 pound-feet of wheel torque. In fourth gear, with a gear ratio of 1.16:1, we're at around 6,900 RPM and producing about 130 pound-feets of torque.

The results are interesting: in third gear, when shifting at 88,800 RPM, we're putting down more wheel torque than in fourth gear, even though our engine speed is lower due to the gear reduction. This means that shifting at redline was a smart decision for this particular scenario. However, if you look at the ratio of wheel torque to peak engine torque (110 pound-feets), dividing 130 by 110 gives us approximately an 18% difference.

This calculation suggests that shifting gears is not as advantageous in fourth gear as it is in lower gears, where there's a greater split between gear ratios. In fact, for most vehicles out there, including our own S2000, the benefits of shifting at redline are more pronounced in lower gears, such as first through third.

A great resource that supports this concept is the book "Physics for Gearheads." This book applies similar principles to a Corvette, using a different methodology but arriving at the same conclusion: shifting gears to redline every time, even in higher gears like fifth and sixth, can optimize acceleration. The authors found that in this specific example, going out to redline was beneficial because it ensured maximum engine torque was available for the next gear.

However, there are situations where shifting at redline might not be ideal. A key consideration is when the ratio of wheel torque to peak engine torque becomes equal across gears. This means that if you're making 8,500 RPM in third gear and producing 102 pound-feets of torque, which is roughly equivalent to the 130 pound-feets of torque in fourth gear at the same speed.

In this scenario, it's not necessary to shift before redline because your engine torque will decrease as you continue accelerating. This makes shifting gears less beneficial, as you'll be producing less wheel torque with each subsequent gear change. So, while shifting at redline can be a good idea for most driving situations, there are cases where it's not the best strategy.

In conclusion, our analysis suggests that shifting gears to redline is a beneficial practice in lower gears like first through third, but may not be as advantageous in higher gears like fourth and fifth. However, if you're looking to optimize your acceleration and engine efficiency, it's worth considering this approach for specific driving situations.

"WEBVTTKind: captionsLanguage: enHELLO EVERYONE AND WELCOMEin this video we're gonna be talking aboutwhen to shift gears in order to maximise accerlerationand so here we what we are doing isour goal is to maximise the force ofthe driven wheels on the groundacross any speed, any rpm whatever gearforce to be as large as possible aswe're accelerating so here we have abeautiful blue Honda S2000 that was veryobvious just from looking at the sketchand so we're trying to maximize thisforce here now two of the assumptionsthat we're going to make we're going toassume that we have infinite tractionswe don't have to worry about that as faras gearing is concerned and we're alsogoing to be assuming we're driving in astraight line so there could be trackswhere for example you're going around acorner and it may not be beneficial toupshift and then downshift again may bebeneficial just leave it in gear orgoing to ignore that we're just going ina straight line we want to know when isthe best time to shift gears based onour p.m. and you're gearing so in orderto maximize this force at the wheels wewant our torque at the wheels obviouslyto be as large as possible so yourengine sends torque back it goes throughthe transmission hits the reardifferential comes to your wheels youwant that torque at the wheels to be aslarge as possible that torque at thewheels is equal to the force that it'sapplying multiplied by the radius ofthat tire so now that we're kind ofchanging this from our goal is tomaximize wheel force we're going tochange that goal to maximizing wheeltorque because they're going toaccomplish the same thing we'll getmaximum acceleration when we havemaximum wheel torque which gives us ourmaximum wheel for us so we need to knowwhat is the equation for the torque atthe wheels within the equation for thetorque at the wheels we have our enginetorque we're going to multiply that bythe gear ratio of whatever gear we arein we're going to multiply that by ourfinal drive ratio and that could also bemultiplied by other gear reductions forexample in the hon s2000 there isanother gear reduction in thetransmission before it gets to the finaldrive and then you will of coursemultiply that by any losses that youhave through the transmission now thelosses will of course apply to everygear and the final drive ratio and thegear reduction are constant so we'rejust going to ignore these because thesearen't really going to change with eachgear our variables here are the enginetorque which of course depends on ourp.m. and our gear ratio which justdepends on which gear you put it in sowe're going to see maxengine torque with the throttle wideopen so moving on we want to maximizethis number right here multipliedtogether engine torque x gear ratio wewant that as big as possible always andthat's going to give us our highestwheel torque so looking at the Hondas2000 gear ratios here I have them onethrough six it's a 6-speed manualtransmission and so our gears here wehave so for example 3.1 33 in first gearversus 2.0 45 in second gear so whatthat means if you take 3.1 3 3 anddivide it by 2 point 0 4 5 there's afifty three percent difference there soyou're going to have fifty three percentmore wheel torque in first gear at thesame engine rpm as you would in secondgear what that of course the drawback tothat is you don't have as high of a topspeed so second gear will go to a higherspeed with less wheel torque first yearwill go to a lower speed with more wheeltorque so in order for this in order foryou to need to shift the torque from theengine has to drop let's say we're goingfrom first to second gear the torquefrom the engine would have to drop fiftythree percent in order for that to beworthwhile which is going to be veryrare as you might imagine so you'repretty much going to run that out toredline so let's look now at a dynocurve so we can now get the exactnumbers and no you know what should wedo when should we shift gears dependingon which gear ship we're on so this Ijust googled Honda s2000 ideally youwould want to die know your vehiclewhich I will do eventually but ideallyyou're going to want to die know yourvehicle that way you can get the exactnumbers but you can just google it getsomething very close I googled s2000dyno sheet this is a 2002 and it was astock vehicle so very close to what Imight find on my own basically whatyou've got nice flat torque curve upuntil about 6000 rpm then vtech changesit to a different cam profile and youget to a higher you know about 130 poundfeet here and then of course as you getto the higher rpms that power starts totaper off and so basically what we'regoing to look at is is this tapering offof the torque when should we shift inthis tapering in order to get back intothis peak torque so ourexample we're going to be in third gearwe're going to go on flat out and we'regoing to want to know you know should wehave shifted at eighty eight hundred rpmwhich is red line so we're going toshift the 8800 rpm and then we're goingto do the math and decide whether or notthat was a good idea so in third gear wehave a gear ratio of 1.4 81 and fourthyear when we shift we have a gear ratio1.16 one so we're at eighty eighthundred rpm and third we want to figureout what RPM that will be and forth sowe just do this simple ratio multiply8800 by one point one six one dividethat by 1.4 81 and that gives us about6,900 our p.m. okay so now what we wantto find out is what is the wheel torquein each one of these gears at this exactmoment so in third gear when we're ateighty eight hundred rpm you can seewe're making 110 pound feet so 1.48 onewhich is our gear ratio x the enginetorque which is 110 10 pound feet givesus 163 pound feet now in fourth gearwith gear ratio of one point one six onewe are going to be at 6,900 RPM sothat's going to be somewhere in thisrange right here as you can see that'sgoing to be about 130 pound feet sowe'll put in 130 pound feet right theremultiply that across and that gives usabout 150 one pound feet so as you cansee 163 is higher than 151 so what thatmeans is in third gear at eighty eighthundred rpm we were putting down morewheel torque than when we shift down tofourth even though we're now at peakengine rpm because of the gear reductionwe're putting down less torque at thewheels so it was a smart decision toshift at redline now the idea ofshifting at redline is actually going toapply to every single gear in my hondas2000 so if you look at 130 and youdivide that by 110 so that's our peakthat's this nice flat area you dividethat by 110 that gives us about eighteenpercent difference and as you can seefrom each one of these gears hereeighteen percent is less of a gearreduction or a torque disadvantage thanchanging gears in any of these so whatthat means is basically run it out tored line and then shift gears and that'sgoing to be the case for you know tonsof youout there especially for your initialgears one through three where there's abigger split between the gear ratios youknow it could get different once you getdown into these but basically for mostcars out there it's going to be the casewhere you're going to want to just runit right out to redline you can do themath yourself and kind of figure it outbut for most vehicles out there becauseof the gearing advantage of the lowergears it's going to be beneficial evenif torque starts to fall off to stay inthat lower gear until you do actuallyhit red line and then shift gears andget back into that peak engine torquebut less wheel torque now a greatresource this book physics for gearheadsI will include a link in the videodescription I've mentioned this beforeit is a really cool book if you're intothis kind of thing they do a verysimilar problem with the Corvette thatused a bit different methodology butanyways they did the same thing and theyfound also that even for this Corvettezo6 2008 you want to go to red lineevery single time gears one through fivebefore shifting and in order to getmaximum acceleration so it generallywill be the case that you'll just prettymuch go out to redline so when would itnot be ideal to shift at redline wellbasically it would be when this numberright here is equal for each gear solet's say you were in third gear at8,500 rpm and we're in the s2000 we'remaking 102 pound-feet well at that pointit's about equal to being in fourth gearwith a gear reduction with 130 poundfeet now this is less than we have herebut this makes the example work so ifyou were at 8,500 rpm and this was yourwheel torque or your engine torquerather what you want to know is that youknow if you keep going past that yourengine torque goes down and as a resultyou're going to be putting less wheeltorque down than if you were to shiftinto fourth so this doesn't happen in mycar but it is the case where you know itwould be ideal to shift before red lineif something like this happened and youwere going for maximum acceleration sothank you guys for watching and if youhave any questions or comments feel freeto leave them below\n"