The Racing Line - Hitting The Apex - Explained

What is the racing line? Why is it important to hit the apex? The racing line attempts to make the largest diameter turning radius in order to minimize lateral g's on the vehicle, thus allowing for greater driving speeds. The idea is to try to make the track into as straight of a line as possible. The math backs this up.
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[@mrdragancelan]

I use this math when I'm at the grocery store to hit the apexes into all the aisles.

[@EyeAmBatman]

+Dragan Celan LOL....180 Jturn, forgot to get milk....

[@rorschach775]

+Dragan Celan there is no purer racing than shopping cart racing

[@hunterreehoorn7831]

+Dragan Celan So Im not the only one who drifts the cart around every corner?

[@tiedomi80]

+Dragan Celan I do this at Costco. XD

[@skidmeister]

I do wall taps and 360 entries too. And sometimes a little rally cross

[@brentstorck3589]

I just want to mention something here. I didn't know jack about vehicles before visiting your channel. Researching the internet, I had hoped to learn a little bit. Finding your channel, I hit the jackpot. You have done an outstanding job with these videos, and I have learned an incredible amount of information. You are by far the best internet-teacher on this subject matter, in my opinion. These videos have allowed me to troubleshoot and fix problems on my own vehicle as well. So, thank you for doing what you do man.

[@darios9797]

props to you sr for using the metric system.

[@Oliver-jv5ww]

+Dario Kruv all science is done in the metric (even in american schools)

[@EngineeringExplained]

+John Doe we used both in nearly all of my classes. It's a reality of the engineering world. No big deal, simple to convert units to work in metric and have much nicer units.

[@darios9797]

Engineering Explained nice, i thought USA used the imperial system for everything.

[@giovannifurfaro9647]

+Dario Kruv Not in the sciences, the scientific community seems to have it together

[@dlobom]

+Engineering Explained That is my experience, text books and teachers mixed units left and right just to keep you on your toes.

[@sayisakindof]

Finally, scientific proof, easy understandable by my non-car friends, now i can shove this to their face and keep hitting the apex! Good work, an excellent channel you have built!

[@EngineeringExplained]

+Miguel Pedro Thank you!!

[@SpacemanXC]

This should be taught in primary schools.

[@Garfield_Osu]

The poor little kids will be so confused tho

[@praadiiit]

Dont, please dont lol 🤣

[@o.megatron2024]

lol the show “Cops” would definitely have more exciting car chases 🤣

[@MJtheFellowActuary]

The fun starts when there are two corners, one after the other. Taking the fastest line through the first corner might compromise your line through the second. It may be wise to take a slower line through the first so that you set yourself up perfectly for the second especially if there is a long straight afterwards.

[@BonniePerez]

Would love to see a vid like the one above for two corners :)

[@JaihindhReddy]

The cleanest video explaining the racing line I found on the inter webs. The green equations were a little hard to read on the white background though. I'm proud.

[@crate2819]

I live my life one apex at a time. Nothing else matters; not the unpaid tickets, not the nagging wife, not the fear my life is basically pointless. For those .5 seconds or less, I'm free.

[@EngineeringExplained]

+Matthew Heagerty We all admire your gallantry.

[@wealllame]

god bless you

[@the_bbq_man9823]

Fast and furious reference?

[@tylerbernius3224]

@@the_bbq_man9823 sounds like it...I hope it is.

[@ElementsMMA]

Amazing

[@soundslave]

I understood some of this.

[@Kenai8000]

im with ya on that one

[@abbybrown3745]

I got lost

[@bscutajar]

It's not even that hard. Are you 12?

[@Kenai8000]

bscutajar correct, its not hard to understand the racing line. Im pretty sure what we are refering to is how quickly he is talking and spewing calculations. That is tough to keep up with and unless you are very sharp minded you wont process it quite fast enough to follow the entire video. As for the insult, it doesnt matter what age the person watching this is. If they are watching this when they are 12 then more power to them. They are probably smarter then you anr I when we were 12. No one likes a douche so dont be condescending.

[@bscutajar]

What calculations? It's just fitting a larger radius and calculating the centripetal force needed from the friction.

[@bleepinjeep]

I think you hit the apex with your vocal speed in this video!

[@HotboiEngineering]

Can you explain when it would be advantageous to take a late apex or early apex in a hairpin or corner? I've seen drivers do this and I don't know why.

[@EngineeringExplained]

+Brap Brap That's a wonderful suggestion!

[@BrandonKent136]

+Brap Brap usually it's better to take a late apex when the next straight away is relatively long. This is to help with maximizing velocity throughout the straight.

[@Dogman36]

it's all about setting the car up perfectly for medium speed or fast corners following the slow one. normally, because they are the slowest corners on the track, a hairpin can be a "throw away" corner that wont affect your lap too much if you dont take the normal line through it, whilst making sure your car is in exactly the right place on the next corner's entry. say, a 180 hairpin right, very short straight, and a 90 degree left. what i'd do is enter the hairpin late and wide, and at such an angle where the car is already aimed at the next apex. it wouldn't be a fast line if say, it were the hairpin and another long straight. there's a video on my channel where you can see this theory in action at the kart track.

[@MrDeapGamingMedia]

+Brap Brap In my opinion, it is probably due because the apex target is the rear tire. Because of that effect, it is easier to late or early apex depending of the car traction layout when accelerating out as you do it before the apex. I could be wrong since I never really raced in real life, but learned by doing many round in many different racing games.

[@TheAmishStig]

+Brap Brap EE will be able to put a lot more math to it, but it's done to optimize the whole track, instead of just one corner. A turn's radius isn't actually 1 radius. It's 2, the entry radius and the exit radius. What moving the apex does is allow those two to not be identical, which changes the characteristics of the corner itself...and affects the racing line of the whole track, rather than just the racing line of a single corner that exists in a vacuum. A late apex makes the entry radius tighter [meaning you have to enter at a slower speed], but makes the exit radius proportionally larger [meaning you have a higher exit speed, and with it, a higher speed at the end of the following straight]. The net effect is that you lose a little time on entry, but spend that much more time accelerating and, if the following straight is long enough and the preceding straight short enough, gain more time by carrying more speed off the turn than you lose by carrying less speed in. An early apex is the exact opposite: the turn-in is a lot shallower than it would be on the basic line, allowing you to overlap braking and corner entry since the wider line raises the bar for how fast is 'too fast'. But it compromises corner exit, so not only are you going to exit slower, you can't actually enter any faster because you need to save some grip to get slowed down for when the radius tightens up. Generally, there's only 3 reasons to apex early: 1) A follow-up corner is close enough that if you exit normally, you'll have overshot the braking zone or entry point for the next turn, compromising not one corner, but 2...or 3, or 4, if it's a big complex and you manage to set off a domino effect. 2) It's being done defensively. The car behind will have to either follow you, run a hugely suboptimal line, or hit you, and done skillfully it costs them more time than it costs you. However, it's risky; if the opponent sees it coming, the technique known as 'up-and-under'...pin your opponent down low, make them to apex early, and then dive under them for a late apex once they've pushed wide and exited slower...is the counter to it. All defensive maneuvers have a counter, so attacking / defending is all about forcing the other guy to make an error you're in position to take advantage of. 3) When you've got an extremely long straight followed by an extremely short one, and extending the full-throttle run via the technique known as trail braking saves you more time than the early apex is costing you on exit. If you're doing 200mph at the start of the braking zone, but won't hit more than 60 before the next braking zone, it's in your best interests to apex early; 1 extra second at 85m/sec covers a lot more ground than several extra seconds accelerating up to 28m/sec. But, you have to be careful not to overshoot the corner; keeping that balance between turning force + braking force under 100% grip means you're not actually turning any faster, you're just braking later and using that wider line to 'save some grip' for braking.

[@seb5945]

I drive everywhere in racing lines. Not everybody gets it but that's ok.

[@nicholasersons]

Fantastic video, the way you explain it with your diagrams makes it so simple to understand. You could not have executed the presentation better than you did!

[@crazydog2580]

hands down my favorite you tuber always great content. very informative but simple enough for general viewers keep it up mate i believe this channel will be come bigger than most :)

[@EngineeringExplained]

+crazydog2580 Thanks!!

[@MadJDMTurboBoost]

If you do a little bit of calculus, you will find that at a certain point, if you can maximize your braking and acceleration (through frictional coefficient, torque, and breaking force) that it is beneficial to brake as late as possible, turn, then accelerate as early as possible. The radius of the turn will be smaller, however, more distance will be covered because braking time, turning, and acceleration time will be at a minimum.

[@drdremd]

Is your whiteboard ok?

[@TigerClaws]

Very clean video, love it!

[@fabiantb]

I'm a big fan of your channel, but this time I have to argue... that it's just the basic theory, but in practice racing drivers follow more of an elliptic path rather than a circle, so that they can brake "into" a corner and accelerate "out" of it. I.e. brake later and accelerate earlier than the circle starts/ends. The downside of it is a tighter and slower apex speed, but the overall speed and more importantly (especially if a long straight comes after) the top speed before and after the corner is higher. The path is elliptic as they balance on lateral and longitudinal tyre load, so gradually step off the brake and tighten the turning circle at the same time and the opposite on the corner exit. Also the early or late apex is also considered, so that drivers dont always touch the inner side of the corner, depending on whether they are defending position or attacking another car. Same strategy applies when there is a long straight after the corner when you sacrifice entry speed to be able to straighten the steering angle and be able to accelerate earlier, i.e. higher top speed on the straight.

[@fabiantb]

+Tibor Fabian : edit: " dont always touch the inner side of the corner" -> dont always touch the middle of the corner, the apex can be early or late.

[@crazychann]

what about multiple corners?

[@stefanradovich8510]

I like your videos man, concise and informative. Taking this apex would only be best if the vehicle has equal acceleration and deceleration, however just about all vehicles will have greater deceleration ability than acceleration. I'm not feeling like crunching the numbers myself atm but wouldn't it be better to opt for a "late apex" as this would offer less deceleration time and more acceleration time. I've got a feeling you'l need to throw down some partial derivatives too, your viewer base seems pretty clever i reckon they could handle it.

[@rawrmeduh]

Dude.. this was intense

[@ChrisKsan]

Good god I have so much to catch up on! I didn't think there was so much science in regards to racing lines and cornering, at least not as detailed! Thank you for this inspirational and informative video!

[@TalenGryphon]

Can you make a video explaining the Scandinavain Flick cornering technique? I (and I imagine many others) am still having trouble understanding how this relates to racing lines, or how the forces involved allow for faster cornering.

[@RaamiKala]

i've never seen the racing line splained like this before..good video jas'

[@Henchman_Holding_Wrench]

I accidentally took a racing line on a left turn during my road test. Lost points because my left wheels rolled over the double yellow lines.

[@Kaisuke971]

"Accidentally" ( ͡° ͜ʖ ͡°)

[@ernestoperez717]

this is the perfect way to demonstrate and teach driving line. this is hew i would have done it.

[@sparco7555]

Good technical explaination.

[@juanpablosaenz7719]

Finally!! Now when my friends say "You still like cars? I thought that was a little kids thing!" I can just send them this and make their mind blow up

[@mrdeath212]

fantastic video. very well explained

[@greasemonkey582]

this is why I'm glad I did all the license challenges on gran turismo. I already know this stuff

[@bobbalm7345]

I must not be the target audience, as you managed to mostly make it more complex for me 😄

[@ClarenceThompkins]

I was just reading this in my Gran Turismo 5 Collector's Book, pretty nice vid

[@dannyrahn7352]

hmmm my understanding of the ideal racing line was a parabolic arc, not a circle. If i'm not mistaken, the reason is that the steering angle is best to keep as low as possible during braking and accelerating at higher speeds to maintain optimal stability and increasing steering angle when approaching and departing the apex when the vehicle reaches its lowest cornering speed. In effect it is possible for the vehicle to decelerate until reaching the apex and then immediately begin accelerating all the while staying as close to the cornering grip threshold as possible. Obviously this would require constant modulation of brake and accelerator on the part of the driver. that's where trail braking and feathering the throttle come into play. do you agree?

[@rahulmanoharan9746]

Thank you for the detailed math

[@joshdenham8404]

I notice some of the best drivers will ever so slightly "exceed" the frictional coefficient of their tires, and use that momentum to help hurdle them around the corner

[@canddmeyer]

Wow, that was a mouthful.

[@gsx-rrider842]

Awsome video man. :) Please do more videos about different racing technics

[@mark33545]

would love to see more of this with muti corner sections

[@jabulaniharvey]

great video...great lap times are all about keeping your average veocity high

[@WOT122]

On the money as always!

[@Ricom69]

In a perfect world this sounds great on on paper. Racers and riders, no need to overthink cornering and mathematics. Get on the bike and practice practice practice. Your brain will determine how well you can take that turn after all the nanosecond decisions are processed. You will eventually improve.

[@nahom6038]

The fastest lines is sometimes different depending on if u have a straight or another corner after the turn, this is correct but in racing late braking and having room to accelerate again forces you to change the "Apex", that's why some corners are faster if u take a late apex and other early apex, and this doesn't apply on hairpin turns for example.

[@bestsceneseverbesthighligh6504]

Wow is this science? why didn't I Learn this in school. I love this 😁😁😁

[@teedjay91]

Since your speed is greater before and after becaus you break and accelerate during the turn, the ideal form should be more like a parabolle than a perfect circle ? so that when you are at your slowest (at the apex) your turn more than before and after.

[@KORTOKtheSTRONG]

+Teedjay Gendron Depending on the car, braking into the turn might not be preferable to braking in a straight line (before the turn)

[@Runner50783]

+Teedjay Gendron It depens on the other variables not taken into account in the video. This video is of course a lab exercise, if this where taking all into account the length of the video would be several hours. But the point has been made clear, you need to cut that apex at the perfect spot in order to get into the corner as fast as possible.

[@teedjay91]

+Abraham Saenz of course, I was just developing the idea by adding the speed variable because it is never constant during a turn. I like the video but 2:46 is short. a 7-8 minutes vidéo could have been great for explaning a bit further

[@REVAMPtheindustry]

+Teedjay Gendron i think we also need to take in account that nobody can drive 'perfectly' and that this theoretical situation EE made up is on a turn that is also perfectly flat, and symmetrical.. and things like a later cut for 'slow in fast out' sometimes doesn't end up being the best choice depending on whats after a given turn.. its good to scrutinize anything if we feel inclined, but i also think the only real problem here is how controlled and 'perfect' this experiment is, leaving the theory sound, but relative in actual application

[@maximdudich]

Euler's spiral would be a good way of finding optimal trajectory.

[@low.est36]

can you please explain how ford flat heads work pretty please i really want to know more about them thanks

[@Baerchenization]

Walter Röhrl says in a few videos that the secret to (at least) driving a 911 fast is to be slowest at the entry in to the corner and accelerating from there on.

[@EyeAmBatman]

Impressive!!!... great to hear the science behind it, I always sketch out my racing lines on a track diagram when racing... never knew the math that was behind it, thanks! :p

[@eliseoquintanilla3908]

Love this video! Great explanation yet again. Love you're stuff!

[@AndrewChilds23]

How about explaining the effect of wider tires and handling? I know the coefficient of friction is not constant in this situation, but I don't know why (I have seen several different explanations), and I feel that it is a very common misconception.

[@MaitreChocobo]

Keep the great work!

[@Archi2g]

Can you add two videos to your long list? What is the difference between a battle tank's V8 engine & a standard road car's V8? When people swap car engines for motorbike engines, how do they go in reverse?

[@NitrousFox]

Thanks for the vid. Very educational

[@Wrchd]

Awesome! Never seen apex stuff done in numbers :)

[@pedro0]

You could explain diferences between small blocks and big blocks! Why use one of them insteaf of the other! And... after your Formula Drift videos, I've been curious about mechanical grip: how to have more of it, what each suspension angle (toe, caster and camber) influences in that mechanical grip and so. Thanks!

[@RyderGaming]

Cool stuff :) I'd watch more of these kind of videos.

[@TheDealinDave]

What if you are in a miata and accelerating isn't that great so you need to take a wide line to have a faster speed but takes you longer to round the corner. I want to know at what point is it more beneficial to not loose speed and take a wider line?

[@ZhangyXD]

when Jesus takes a corner, he doesn't hit the apex. He makes one!!

[@albertsewell878]

have done a e85 gas explained and how they are making power with it??

[@pwoodson21]

First!.. thank you for including the engineering behind the concept besides just explaining what to do

[@MrMelgar2000]

Could you also make a different video involving different drive train layouts of cars (4WD, FR, FF, ETC.)? And how these affect how the vehicle should enter and exit a corner?

[@MajdSindi96]

Hey Jason, Can you do a video on heel-toe? How to and benefits

[@PTReDaLeRtPT]

How much a non-circular turning approach with a late apex can improve the exit speed after the apex?

[@bambinodeskaralhes]

It's not so simple, I'll make a more complete analysis: we know that the green line and the red are the same until the green starts to decelerate. Imagine the two cars are at top speed (V). The first must brake (due to torricelli equation) ((V^2 - g*u*Rg) / 2*g*u) = Dg meters behind the curve begin. The red on the other side must brake at (V^2 - g*u*Rr) / 2*g*u = Dr meters behind. Let's compute the total time the green line driver takes to brake, turn until -90 degres. The time it takes to brake is one root of the given quadratic equation: -(g*u/2)*(Tb_g)^2 + V*Tb_g - Dg = 0 And the time the green tracer takes to turn -90 degres inside the curve of radius Rg is: (pi/2)* Rg / sqrt( g*u*Rg) = Tc_g The total time it takes for braking and making the curve is given as follows: Tt_g = Tc_g + Tb_g Beyond that we have that the time the red tracer takes to make his trajectory is the sum of the time that he takes to transverse the space while green tracer is braking, the time he takes to brake and the time he takes for making the curve, plus the time for accelerating and getting to the end curve position of the green line. these are given respectively by: (40m + Dg - Dr) / V = Tnb_r = time the red tracer takes at top speed not braking -(g*u/2)*(Tb_r)^2 + V*Tb_r - Dr = 0 = equaton that gives the time the red tracer takes for braking (pi/2)* Rr / sqrt( g*u*Rr) = Tc_r = time the red tracer takes making the curve (g*u/2)*(Ta_r)^2. + sqrt(g*u*Rr) * Ta_r = 40m = time the red tracer takes for reaching the end curve position of green tracer Tt_r = Tnb_r + Tb_r + Tc_r + Ta_r the comparison between the total times tells us which trace is better. Lets put the data informed by the author and resolve the equations. g = 10m/s² ; u = 1 ; V = 42m/s (150km/h for instance) ; Rg = 80m ; Rr = 30m so I have solved all the equations given above and obtained the results: Dg = 48.2m ; Dr = 73.2m ; Tb_g = 1.37157s ; Tb_r = 2.46795s ; Tc_g = 4.4428s ; Tc_r = 2.7207s ; Tnb_r = 0.3571 ; Ta_r = 1.58455s ; Tt_g = 5.8144s ; ; Tt_r = 7.1303s So as you can see, for around 150km/h (42m/s) it's more interesting to get the 80 meters radius curve instead of the 30 and the green pilot gets an advantage of 1.3159s I did the calculations too for V = 252km/h (70m/s) and the values obtained were: Dg = 205m ; Dr = 230m ; Tb_g = 4.17157s ; Tb_r = 5.2679s ; Tc_g = 4.4428s ; Tc_r = 2.7207s ; Tnb_r = 0.2143s ; Ta_r = 1.58455s ; Tt_g = 8.61437s ; Tt_r = 9.78745s Which turns out to be a worse time difference for the green pilot, this time only 1.173s. So top speed in this situation, without downforce considerations, tends to contribute less for the time difference between the two trajectories.

[@milaanvigraham8664]

By the way are you sure it's 80m? I did the math and got 60+20(2^0.5)

[@xyphenius9942]

How do you calculate the racing line? As in, how to calculate a circle that is bounded buy two smaller ones, like in your video?

[@amcheung10]

Hi could you possibly do a video on wheel spacers and the pros and cons of them?

[@gokartbuyer]

+amcheung10 Bye bye wheel bearings along with bye bye tire.

[@po.russki]

I second this!

[@xopexindustries]

Where would the apex be for a highway on or off ramp that is more than 90 degree's?

[@acjtwo]

Engineering Explained I have a question for you please; What happens (benefits vs cons) when you change factory tires to different sizes? I had 225-40-18 changed to 225-45-18 ? Leon Cupra 265 hp DSG thanks!

[@koolio143]

the video was reaaally fast. Taking your time to go through things would certainly make me enjoy the video more.

[@EngineeringExplained]

+C.D. I took the racing line.

[@koolio143]

+Engineering Explained Touché. hahah I take it back. It was perfectly executed!

[@stevenswm9844]

This kinda reminds me of the "Dukes of Hazzard" theme song, when they refer to "straightening the curves", though I'm not for sure that taking the racing line is what they are referring to! haha

[@fatboySRK]

I learned this in the original **Nintendo** players guide as a kid in the 80s. Seriously. The guide covered this exact approach, without the academic explanation of course, for approaching corners in Rad Racer. See below. i16.photobucket.com/albums/b13/TheCarpenter/RadRacerONPG.jpg Thanks for the vid. A+

[@jamiechestnutfineart]

Only watched this for when I play racing video games...

[@jonathanrandall2547]

What about double apexes? What is the point of them and when does a driver use them?

[@federicomontoya1364]

Hey man! Awesome stuff. Would you mind illustrating me how would this work on zapcat racing? RIB boats with arm tillers. Thanks mate!

[@Catalyph]

How does the corner being slopped affect this? or does it at all ?

[@Phillguy]

You forgot about all whell drive man... that just kills it....

[@imbunche2008]

80 m isn't bad, but it's actually possible to drive in an arc with radius = 60 + 20√2 ≈ 88.3 m without leaving the road. That increases the maximum speed to almost 66 mph.

[@Jackisaboss1208]

Wouldn't the further distance traveled due to the greater radius mitigate some of the advantage that you gain due to the higher velocity? Wouldn't the racing line ideally take into account both the distance traveled and the maximum velocity? Thanks in advance

[@bluasterisk]

I appreciate these videos, makes studying physics a lot more fun :D

[@rockybarry]

I was wondering all this time what an apex in racing is and I happen to already know all of this...

[@sjkdec18]

What about the different distances in the lines?

[@shubhamsurve113]

Can you explain about brakes calculation?

[@Teach_EM]

I'm currently a mechanical engineering student and was wondering if someone could help me understand something. In all my engineering courses, the acceleration due to gravity is given to us as 9.81m/s^2 but in all my other courses such as math and physics courses, it is given to us as 9.8m/s^2 or 9.80m/s^2. So I'm just wondering why we use a higher value for the engineering problems. I understand that the acceleration due to gravity is dependent on altitude, but it really only has a noticeable effect at high altitude. Is it just to be safe, or is there another reasoning behind it? Thanks

[@isacnr7]

wow much info

[@DrR1pper]

The problem is though that the V1 line completes the 90 degrees of turning 39% quicker than the V2 line due to the shorter distance of travel.

[@struyvenstefaan]

Much more important is how fast can you hit the throttle On the race line explained here it is only starting from the apex in the middle of the turn If however you put the apex later in he turn and if you steer in later, than you can hit the throttle much further Whitch will result in a higher exit speed

[@dimdimis2936]

There 's a huge mistake in this approach-theory. The mistake is that suddenly with the wheel in the straight you must change the direction immediately and the car is placed upon the R=80m arc. That can't be done practically. The wheel cannot be turned from 0 degrees to, let's say, 30 degrees of angle. in a blink of an eye. It's turned gradually. The time spending for turn the wheel from 0 to 30 degrees, the car is moving to an ellipse, called clothoide. After that you enter to an arc with steady radius smaller than 80 degrees. That means that the turn in point is move back, as also the exit point moves front. Only apex point stays same.

[@dotmac9789]

Useful

[@saivineet9810]

How did you get the number 80 for 40 and 20???which mathematical concept are you using?

[@joeyflannery6053]

How would this relate to oval racing then?

[@JoeIsCrazyWillman]

I find the hardest to calculate for is your 3/4 or more turns. 90° no problem. U-turns aren't that bad... But when you gotta turn 270+ degrees, or even a full 360 (such as up or down hill and pass over/under where you started the turn... That's where I lose sight and knowledge of how to Apex and even realistically where the Apex actually is. In a full 360, hard to call it an Apex when it's more like a loop not a corner. So how do you approach those particularly long, extra degreed turns?

[@widfo_moto7345]

The racing line isn't always the fast line. You're describing the ideal fast line, not a racing line. Also as you mention, the traction circle of the car changes depending on setup further changing the line :P

[@EngineeringExplained]

+Chris Davis I'm describing the ideal geometric racing line, but that doesn't necessary mean it's the fastest line. This of course gets more complicated and depends on the vehicle, if it has more power it may be beneficial to hit a late apex to straighten out and take advantage of the fact that the vehicle can make up lost time with faster acceleration. Basics first, as always, Chris. :)

[@MrRepairmanjack]

Although %5 may seem insignificant, I feel that 0.5 of a second is a lifetime when measuring 0 to 60 times. How much power must be added to a 3000lbs car to decrease its 0 to 60 time from 7.5 to 7.0 seconds?

[@Mrcloc]

But this is assuming a constant speed corner. How does this compare to a slow in, fast out line?

[@two_number_nines]

im nfs and real racing 3 expert and you cant use brakes from entry to the apex and keep the same radius of steering. gaming real racing 3, nfs and gta 2001-2006 learned me that it is best to start using brakes very early then when entering corner and doing racing line leave the gas and the brakes do nothing until i go 2-7 meters after the apex and slam on throttle. the higher the speed of the car, less the corner angle and wider the track the early i accelerate. i dont like braking to the apex and then slam the gas instantly because when braking i have 2 forces trying to make the tyres slip 1st is centrufugal force and 2nd is the force cause by the mass of the veichle, which means while braking i can take less centrufugal force before slip than if i keep constant speed and this way increasing exit speed. the method is suitable for high steer angle corners after which there is long straight road

[@xmviv]

Thanks

[@epicg5554]

Where did you get 9.81^2 from??

[@ttofaudishanghai]

great video mate, really liked it. just a question always had, how would you justify karting line and f1 lines, and why do rally cars drift, but to uses the full friction eclipse? thanks a lot

[@sticksen]

This video is more about the qualifying line, not the racing line. In the racing line, you're also focussed on blocking off other racers behind you, not only the optimal speed for the bend.

[@ZBTEproductions]

+sticksen It's still called the racing line. In racing situations, you have to adapt the racing line to drivers alongside you, and attacking/defending lines.

[@voidhabit8438]

Is the Racing Line, the same as The Brachistochrone ?

[@wholeass83]

I love how I figured this math in my head without being taught when I got my license just from driving and calculating in my head.