"Speed costs money. How fast can you afford to go?"
Honestly answering that question is the first step in deciding what sort of car and engine you're setting out to build, else you will likely spiral into a constant game of second guessing yourself - looking for more and more power - that at best will cause you to spend more than you have to and at worst will prevent you from ever actually finishing your car!
It takes at most 50 horsepower for a typical mid-size car to cruise at 100 mph. The BMW Z3 coupe - with similar size and aerodynamics as our beloved S30, and with 228 crank horsepower (in the ballpark of a stout L28 street build) - has a top speed of 155mph. Any modern car can easily reach the century mark - even though in most of the US you can't drive faster than about 85 mph without losing your license. On the street, top speed is not nearly as important as acceleration: how quickly can you speed up to change lanes or merge into highway traffic or pass a lumbering truck on a two lane road.
Note: this article is aimed at street driven cars; there may be some useful info for road racers and drag racers, but if that's where your interest lies you'll have to fill in some gaps on your own.
Lets start with the basics. If you drop a rock off a tall building gravity pulls it towards the ground causing the rock to accelerate - increase it's speed - at a constant rate: every second the rock falls its downward speed increases by 32 feet-per-second until it actually hits the ground. After 1 second the rock is falling at a speed of 32 feet/sec, after 2 seconds its falling at 64 feet/sec, and after 2.75 seconds it is falling at 88 feet/sec, which happens to be 60mph. We call the acceleration of gravity - 32 feet-per-second-per-second - 1 gravity - or 1G (its really 32.2 ft/s^2, but 32 is close enough for government work).
When it comes to cars, the force applied by the drive wheels will cause the car to accelerate forward.
Automotive acceleration is traditionally measured by 0-60mph times (or 0-100kph times if you prefer metric units). Flat-out 0-60mph sprints aren't very common in every day driving; it was just an easy to measure number that the car magazines latched onto and has taken on an outsized importance. Still, it gives us a place to start.
It takes at most 50 horsepower for a typical mid-size car to cruise at 100 mph. The BMW Z3 coupe - with similar size and aerodynamics as our beloved S30, and with 228 crank horsepower (in the ballpark of a stout L28 street build) - has a top speed of 155mph. Any modern car can easily reach the century mark - even though in most of the US you can't drive faster than about 85 mph without losing your license. On the street, top speed is not nearly as important as acceleration: how quickly can you speed up to change lanes or merge into highway traffic or pass a lumbering truck on a two lane road.
Note: this article is aimed at street driven cars; there may be some useful info for road racers and drag racers, but if that's where your interest lies you'll have to fill in some gaps on your own.
Lets start with the basics. If you drop a rock off a tall building gravity pulls it towards the ground causing the rock to accelerate - increase it's speed - at a constant rate: every second the rock falls its downward speed increases by 32 feet-per-second until it actually hits the ground. After 1 second the rock is falling at a speed of 32 feet/sec, after 2 seconds its falling at 64 feet/sec, and after 2.75 seconds it is falling at 88 feet/sec, which happens to be 60mph. We call the acceleration of gravity - 32 feet-per-second-per-second - 1 gravity - or 1G (its really 32.2 ft/s^2, but 32 is close enough for government work).
When it comes to cars, the force applied by the drive wheels will cause the car to accelerate forward.
Automotive acceleration is traditionally measured by 0-60mph times (or 0-100kph times if you prefer metric units). Flat-out 0-60mph sprints aren't very common in every day driving; it was just an easy to measure number that the car magazines latched onto and has taken on an outsized importance. Still, it gives us a place to start.
If we assume acceleration is constant, its easy enough to convert between 0-60mph times and acceleration in physical units such as feet/sec^2 or G's:
acceleration = change-in-speed / time, or re-arrange: time = change-in-speed / acceleration
Units are always important: 60mph is 88 feet/second, and G is 32 feet/second/second. A real world example: Car&Driver got the (somewhat porky - 2900 pound) 2017 Civic Si to 60mph in 6.7 seconds:
acceleration = 88 ft/sec / 6.7 seconds = 13.1 feet/sec/sec, 13.1 / 32 = .41G
Thanks to modern technology even the most under-powered econobox (I'm looking at you Toyota Yaris) can manage 0.3G of acceleration.
0-60 time = 88 feet/second / (0.3 x 32 feet/second/second) = 9.2 seconds
Plugging in a few different numbers for acceleration gives us a chart of equivalent 0-60 times:
The fastest of today's FWD hot-hatches can do 0-60 in the low 6 second range, the BMW Z3 I mentioned earlier manages it in 6-seconds flat, modern muscle cars like a Mustang or Camaro can do it in a hair under 4 seconds, and some of the quickest super-cars can do 0-60 in the low 2s - they can accelerate forward faster than a falling rock! By comparison, 1970s Porsche 911s went 0-60 in what is today a pretty pedestrian 7.5 seconds, and when showroom new our Z cars were in the mid 8-second range!
Acceleration is limited by both tire traction and power. Lets take those one at a time.
Traction comes down to friction between the tire and the road. A lot of college physics books claim the coefficient of friction for rubber on concrete is 0.8, meaning a rubber tire can apply a maximum forward force of 0.8 times the weight pressing down on that tire before it starts to slip/spin. If you do a little physics, for a car with 2 driven wheels carrying 50% of the weight of the car, the maximum acceleration in G's is half the coefficient of friction - or in this example about 0.4G - equivalent to a 6.9 second 0-60 time.
If that is the traction limit, how does any car ever go 0-60 in less than 6.9 seconds? The model of friction in those physics books is a bit of an oversimplification based on one hard smooth surface resting on another. A 0.8 coefficient of friction is realistic for the hard narrow tires that were state of the art in the 1960s and 70s when a lot of those physics books were written - but wider tires and softer rubber can yield higher coefficients - even greater than 1.0 (something some introductory physics books suggest is impossible). Modern performance-oriented street tires have coefficients in the ballpark of 1.0-1.1 and extra wide ultra-soft compound "max-performance" tires can push that to at least 1.3. The 2018 V8 powered Ford Mustangs have 12 inch wide performance tires on the back and manage .7G of acceleration.
Another piece of this puzzle is weight distribution. Putting more of the car's weight on the driving wheels means those wheels can deliver more forward force on the car, yielding greater acceleration. Mid-engine supercars put about 60% of their weight on the rear driving wheels, which combined with super-wide super-soft tires is a big part of how they achieve sub-3 second 0-60 times. Our Z's have close to a 50/50 front/rear weight distribution, thanks mostly to the big gas-tank in the rear, which is pretty good for a front-engine rear-wheel-drive car. With the engine and transaxle up front, a front-wheel-drive car puts 60% (or more) of its weight on the driving wheels, compared to 50% or less for a front-engine RWD car, giving FWD an edge. Under acceleration, weight is transferred to the rear wheels, which helps a RWD car and hurts the FWD car, but for practical purposes the transfer isn't enough to offset the FWD advantage.
Having 4 driven wheels is better than 2, allowing 1G or more of acceleration on street tires. This is how the Subaru STIs can rival the Mustang's 0-60 times without the big V8 horsepower (the Subie does 0-60 in 4.6 seconds with "just" 310 crank horsepower); unfortunately 4WD is not exactly a bolt-on mod.
Now lets talk about power. Acceleration requires power, and the power required goes up with both the car's speed and acceleration. At low speeds where air drag is negligible there is a simple relationship:
Power = mass x velocity x acceleration
We can use this to get a pretty good estimate of the power required for a 0-60mph dash. Its easiest to use metric units:
Power = 1200Kg x 26.8m/sec x (.47 x 9.8m/sec/sec) = 148,129 Watts
Divide by 745.7 Watts per horsepower to get 199 (wheel) horsepower.
This is the power needed to accelerate (at .47G) the last little bit to 60mph; it is the maximum horsepower needed in a .47G 0-60mph sprint. This assumes the car is geared to deliver that 199hp at 60mph, and that the driver is able to keep the throttle right on the edge of wheel spin the whole way to 60. I'll dig into the gearing part of this story in another post but for now we have a way to estimate what we need in the way of tires and engine mods to reach a particular 0-60 target.
So you might be thinking "a 6-second 0-60 time is pretty darn quick, why does anyone build an s30 with more than 200whp?" Which reminds me of an old joke about dogs with the punchline "Because they can!" Having more power, especially in the mid-RPMs (what we usually mean when we think of a torquey engine) can give us more acceleration in 3rd or 4th gear at speeds beyond 60mph - e.g. for making a quick pass on the interstate. But mostly, you only need more power if you are racing and need lots of acceleration beyond 100mph.
Or if you have a lot of traction. A new V8 Mustang with all the go fast options can do 0-60mph in about 3.9 seconds (.7G of acceleration). Not surprisingly, the Mustang is packing 460 crank horsepower and 12inch wide rear tires - about 50% wider than the typical Z-car tire. A Z-car with similar 12 inch tires (and fender flares to clear them) should have enough traction to match the Mustang, but lets look at the power requirement:
Power = 1200Kg x 26.8m/sec x (.7 x 9.8m/sec/sec) = 220,618 Watts = 296whp
Assuming a 15% power loss in drive-train friction, that's about 350 crank horsepower - a lot to squeeze from a streetable 2.8 liter NA engine.
Real world complications: When you dig into the numbers for a Z car with typical NA power levels, you find that the cars are usually traction limited in 1st gear and power limited in 2nd gear. If you take the car with 200whp from the example above and fit a wider rear tire - lets say an "ultra performance" 225mm tire - the car will be able to accelerate harder in 1st gear and turn a quicker 0-60 without adding more horsepower. The math is more complicated and depends on gearing and how much stickier the wider tire is, but increasing max acceleration from .47 to .55G while keeping the same 200whp can knock about 0.4 seconds off the 6 second 0-60 time. The thing is this is mostly 1st gear improvement: without more horsepower the bigger tires won't generate any more acceleration in 2nd gear or above; the wider tires help at the drag strip but won't help with merging at the end of the on-ramp.
Back to How Fast is Fast? What we usually think of as "speedy" in a street car - after "can it spin the tires" - is how well the car accelerates when downshifting a gear for a quick pass. Without a turbo or big V8 displacement, beyond 2nd gear and 60mph there just isn't enough power available from an NA L6 for extreme acceleration, especially given the rapidly increasing aerodynamic drag soaking up more and more power. In general the more horsepower the engine can provide the better - again with the caveat that the gearing needs to allow the engine to make the power where its needed.
Lets look at this scenario in a little more detail: if we had that hypothetical 200whp L-6, what acceleration do we see in 4th gear at 75mph? Gearing plays a part here, but 4th gear at 70mph corresponds to about 4000RPM, and about 120whp.
The big take-aways from all of that is that trying to build an NA L6 Z-car that can keep up with a modern performance car is hard; it requires an impractical amount of horsepower from the L6, really wide tires, and most of that performance can't really be used on the street. If that kind of performance is your goal you really need a turbo engine or V8 swap. But making enough horsepower to be quicker than 99% of everyday traffic isn't all that hard, and can make for a fun-to-drive car - and that 200whp is what I am aiming for.
There are also a few surprises when we look at gearing, but that's another story.
acceleration = change-in-speed / time, or re-arrange: time = change-in-speed / acceleration
Units are always important: 60mph is 88 feet/second, and G is 32 feet/second/second. A real world example: Car&Driver got the (somewhat porky - 2900 pound) 2017 Civic Si to 60mph in 6.7 seconds:
acceleration = 88 ft/sec / 6.7 seconds = 13.1 feet/sec/sec, 13.1 / 32 = .41G
Thanks to modern technology even the most under-powered econobox (I'm looking at you Toyota Yaris) can manage 0.3G of acceleration.
0-60 time = 88 feet/second / (0.3 x 32 feet/second/second) = 9.2 seconds
Plugging in a few different numbers for acceleration gives us a chart of equivalent 0-60 times:
- 0.3G = 9.2 seconds
- 0.4G = 6.9 seconds
- 0.47G = 6 seconds
- 0.5G = 5.5 seconds
- 0.55G = 5 seconds
- 0.6G = 4.6 seconds
- 0.7G = 3.9 seconds
The fastest of today's FWD hot-hatches can do 0-60 in the low 6 second range, the BMW Z3 I mentioned earlier manages it in 6-seconds flat, modern muscle cars like a Mustang or Camaro can do it in a hair under 4 seconds, and some of the quickest super-cars can do 0-60 in the low 2s - they can accelerate forward faster than a falling rock! By comparison, 1970s Porsche 911s went 0-60 in what is today a pretty pedestrian 7.5 seconds, and when showroom new our Z cars were in the mid 8-second range!
Acceleration is limited by both tire traction and power. Lets take those one at a time.
Traction comes down to friction between the tire and the road. A lot of college physics books claim the coefficient of friction for rubber on concrete is 0.8, meaning a rubber tire can apply a maximum forward force of 0.8 times the weight pressing down on that tire before it starts to slip/spin. If you do a little physics, for a car with 2 driven wheels carrying 50% of the weight of the car, the maximum acceleration in G's is half the coefficient of friction - or in this example about 0.4G - equivalent to a 6.9 second 0-60 time.
If that is the traction limit, how does any car ever go 0-60 in less than 6.9 seconds? The model of friction in those physics books is a bit of an oversimplification based on one hard smooth surface resting on another. A 0.8 coefficient of friction is realistic for the hard narrow tires that were state of the art in the 1960s and 70s when a lot of those physics books were written - but wider tires and softer rubber can yield higher coefficients - even greater than 1.0 (something some introductory physics books suggest is impossible). Modern performance-oriented street tires have coefficients in the ballpark of 1.0-1.1 and extra wide ultra-soft compound "max-performance" tires can push that to at least 1.3. The 2018 V8 powered Ford Mustangs have 12 inch wide performance tires on the back and manage .7G of acceleration.
Another piece of this puzzle is weight distribution. Putting more of the car's weight on the driving wheels means those wheels can deliver more forward force on the car, yielding greater acceleration. Mid-engine supercars put about 60% of their weight on the rear driving wheels, which combined with super-wide super-soft tires is a big part of how they achieve sub-3 second 0-60 times. Our Z's have close to a 50/50 front/rear weight distribution, thanks mostly to the big gas-tank in the rear, which is pretty good for a front-engine rear-wheel-drive car. With the engine and transaxle up front, a front-wheel-drive car puts 60% (or more) of its weight on the driving wheels, compared to 50% or less for a front-engine RWD car, giving FWD an edge. Under acceleration, weight is transferred to the rear wheels, which helps a RWD car and hurts the FWD car, but for practical purposes the transfer isn't enough to offset the FWD advantage.
Having 4 driven wheels is better than 2, allowing 1G or more of acceleration on street tires. This is how the Subaru STIs can rival the Mustang's 0-60 times without the big V8 horsepower (the Subie does 0-60 in 4.6 seconds with "just" 310 crank horsepower); unfortunately 4WD is not exactly a bolt-on mod.
Now lets talk about power. Acceleration requires power, and the power required goes up with both the car's speed and acceleration. At low speeds where air drag is negligible there is a simple relationship:
Power = mass x velocity x acceleration
We can use this to get a pretty good estimate of the power required for a 0-60mph dash. Its easiest to use metric units:
- A 2600 pound Z-car masses 1200Kg.
- 60mph is 26.8 meters/second
- 1G is 9.8 meter/second/second
- 1 horsepower is 745.7 Watts
Power = 1200Kg x 26.8m/sec x (.47 x 9.8m/sec/sec) = 148,129 Watts
Divide by 745.7 Watts per horsepower to get 199 (wheel) horsepower.
This is the power needed to accelerate (at .47G) the last little bit to 60mph; it is the maximum horsepower needed in a .47G 0-60mph sprint. This assumes the car is geared to deliver that 199hp at 60mph, and that the driver is able to keep the throttle right on the edge of wheel spin the whole way to 60. I'll dig into the gearing part of this story in another post but for now we have a way to estimate what we need in the way of tires and engine mods to reach a particular 0-60 target.
So you might be thinking "a 6-second 0-60 time is pretty darn quick, why does anyone build an s30 with more than 200whp?" Which reminds me of an old joke about dogs with the punchline "Because they can!" Having more power, especially in the mid-RPMs (what we usually mean when we think of a torquey engine) can give us more acceleration in 3rd or 4th gear at speeds beyond 60mph - e.g. for making a quick pass on the interstate. But mostly, you only need more power if you are racing and need lots of acceleration beyond 100mph.
Or if you have a lot of traction. A new V8 Mustang with all the go fast options can do 0-60mph in about 3.9 seconds (.7G of acceleration). Not surprisingly, the Mustang is packing 460 crank horsepower and 12inch wide rear tires - about 50% wider than the typical Z-car tire. A Z-car with similar 12 inch tires (and fender flares to clear them) should have enough traction to match the Mustang, but lets look at the power requirement:
Power = 1200Kg x 26.8m/sec x (.7 x 9.8m/sec/sec) = 220,618 Watts = 296whp
Assuming a 15% power loss in drive-train friction, that's about 350 crank horsepower - a lot to squeeze from a streetable 2.8 liter NA engine.
Real world complications: When you dig into the numbers for a Z car with typical NA power levels, you find that the cars are usually traction limited in 1st gear and power limited in 2nd gear. If you take the car with 200whp from the example above and fit a wider rear tire - lets say an "ultra performance" 225mm tire - the car will be able to accelerate harder in 1st gear and turn a quicker 0-60 without adding more horsepower. The math is more complicated and depends on gearing and how much stickier the wider tire is, but increasing max acceleration from .47 to .55G while keeping the same 200whp can knock about 0.4 seconds off the 6 second 0-60 time. The thing is this is mostly 1st gear improvement: without more horsepower the bigger tires won't generate any more acceleration in 2nd gear or above; the wider tires help at the drag strip but won't help with merging at the end of the on-ramp.
Back to How Fast is Fast? What we usually think of as "speedy" in a street car - after "can it spin the tires" - is how well the car accelerates when downshifting a gear for a quick pass. Without a turbo or big V8 displacement, beyond 2nd gear and 60mph there just isn't enough power available from an NA L6 for extreme acceleration, especially given the rapidly increasing aerodynamic drag soaking up more and more power. In general the more horsepower the engine can provide the better - again with the caveat that the gearing needs to allow the engine to make the power where its needed.
Lets look at this scenario in a little more detail: if we had that hypothetical 200whp L-6, what acceleration do we see in 4th gear at 75mph? Gearing plays a part here, but 4th gear at 70mph corresponds to about 4000RPM, and about 120whp.
- 120hp = 89500 watts
- mass of the car is stil 1200Kg
- 75mph = 33.5 meters/sec
Rearrange the formula:
acc = power / (mass * velocity) = 89500 W / (1200Kg * 33.5 m/s) = 2.2 meters/sec/sec = .22G
This doesn't sound like a lot, but remember, its about twice what typical traffic reaches. Having enough power to spin the tires at highway speeds sounds cool, but there is no good reason to do it and its a good way to lose control of the car. Having a bit more acceleration might be nice - and if you really need it, it is available in 3rd gear (75mph in 3rd is about 5200RPM, near a typical L6 power peak).
acc = power / (mass * velocity) = 89500 W / (1200Kg * 33.5 m/s) = 2.2 meters/sec/sec = .22G
This doesn't sound like a lot, but remember, its about twice what typical traffic reaches. Having enough power to spin the tires at highway speeds sounds cool, but there is no good reason to do it and its a good way to lose control of the car. Having a bit more acceleration might be nice - and if you really need it, it is available in 3rd gear (75mph in 3rd is about 5200RPM, near a typical L6 power peak).
The big take-aways from all of that is that trying to build an NA L6 Z-car that can keep up with a modern performance car is hard; it requires an impractical amount of horsepower from the L6, really wide tires, and most of that performance can't really be used on the street. If that kind of performance is your goal you really need a turbo engine or V8 swap. But making enough horsepower to be quicker than 99% of everyday traffic isn't all that hard, and can make for a fun-to-drive car - and that 200whp is what I am aiming for.
There are also a few surprises when we look at gearing, but that's another story.
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