How Fast is Fast?

There is an old saying among hot-rodders and racers: 

"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.

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:

• 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

Before we get too wrapped up in 0-60 times, note that even fast moving traffic typically accelerates at maybe 0.1G. I put a G-meter app on my smart phone and on my rush hour commute I never hit more than about .25G, and not for very long. If you pulled 0.5G with your spouse in the car they would probably yell at you to stop so they could get out and walk home.  The main value in 0-60 is that it gives us a feel for how quick a car feels compared to other cars with similar 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:

• 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

For a 6 second 0-60, we need .47G of acceleration - about the best we can hope for from a near stock-size (205mm wide) street tire.

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).

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.

Do you really want a silk purse?

When I was a snot-nosed kid growing up in small town Pennsylvania, having your own car was the Holy Grail of high school life. Unless your parents were especially well-off and especially generous, having a car at age 17 meant saving up several years of less than minimum wage income, buying a worn-out car and then learning to wrench it back to life. One of the things we learned kind of quickly was that the actual wrenches came in 3 varieties:

• No-name stuff they sold at the no-name discount store that were really cheap and quickly broke.
• The shiny Proto tools hanging on a big display behind the counter at the NAPA store; the chrome would have looked at home on a '57 Chevy. These were really pretty and never broke, but you could spend a whole week's paper-route money on a single socket!
• And then there were Craftsman brand tools from the Sears store. Less than half the price of the Proto stuff, not quite as shiny but with the same lifetime guarantee (this was back in 1976 - sadly things have changed -  the quality of Craftsman tools has slipped and Sears itself is on shaky ground). Like a lot of my friends, the Christmas after I turned 16 I got the 100-piece Craftsman tool set under the tree - 1/4, 3/8 and 1/2 inch drive ratchets and sockets and a set of combination wrenches in a nice steel toolbox.  I think back in 1976 that set cost all of $99. And I still have most of those wrenches today!

What does this little trip down memory lane have to do with old Datsuns? Simple enough, whatever part you want to buy or repair you want to make, there will usually be 3 options: something cheap that will quickly wear out or break, something fancy and really expensive, and something that is not cheap or fancy but will work well and last forever.

A lot of the folks you'll find working on old cars have technical backgrounds: there are the unsurprising machinists and mechanics and engineers, but also computer programmers and finance guys and various kinds of health care workers. They tend to be the people who have to be fanatical about doing thieir job just right. Doing a half-way job on a car that you are passionate about is unthinkable, but doing everything to perfection uaully means never getting to the point of having a car that you can drive and have fun showing off and taking places. When you're planning out a restoration or engine build it is tempting to go for all the fancy stuff. For any one part its often just a few dollars more, and when you're going back and forth between which thing to buy you start thinking "I'm only going to buy it once, I might as well go for the best". The hidden gotcha is that by adding 20% (or more) to the cost of everything, you're likely stretching out the day when you have the money to actually finish the car - if you don't lose interest before that happens!

Its not just money, sometimes its actually time. This occured to me in the middle of a project to spiff up the interior of my 260Z. I had bought new seat covers and foam seat inserts from Banzai Motorworks and the fellow who runs the place recommended ACC Carpets. They had reasonable prices, so I bought a set - no hassles, came quickly. Then I pulled the old carpets out, and while the floors were still pretty solid there was some ugly rust where the floor pans were welded together and a spot under the passenger seat where I suspect someone spilled something corrosive (maybe a Coke?) many years ago. No problem, I think - I'll just use one of the rust converters to clean them up and put a coat of "rust encapsulating" paint on them before I put the carpets in.

After a couple weekends this job just got bigger and bigger.  The jute padding on the transmission tunnel smelled like a wet dog - I pulled it up and used Goof-Off glue remover to cleanup the paint underneath.  The sound deadening "tar mats" were removed - through a combination of dry ice (about $50 worth), heatgun (had  to buy that too) and a putty knife (I  thankfully already had). I read up on rust-converters and bought a gallon jug of Evaporust and followed the directions: spread paper towels over the rusty floors, soak it with the Evaporust liquid and cover with plastic garbage bags to keep it from drying out. The rust came up, but slowly. Sanded some of the worst pitted areas and applied a heavier dose of Evaporust. Started to see bare metal. Switched to MetalBlast, a  phosphoric acid based product that removes and neutralizes rust and etches the steel in preparation for paint (it also removed a lot of the remaining factory paint). And finally I brushed on two coats of RustBullet.

Before

Evaporust followed by Metal Blast

A lot of rust removed

After two months of weekends the floors look better - 45 years of crud have been removed, 95% of the rust is gone and there is paint covering bare metal - but to be very honest it doesn't look like the professionally sand blasted and epoxy sprayed interiors you see on the $50,000 restorations on the intenet. And oh-crap, I've been crawling in and out of the car so much that the ancient weatherstripping on the door frames - which weren't all that bad to start with - have started to disintegrate.

Two coats of Rust Bullet

This is where you have to apply the "silk purse" thinking. How important is removing all of the surface rust from the floor - that is just going to be covered up with a carpet? On a car that never goes out in bad weather? When I'm an old guy who will be lucky to still be driving  a car with no power steering 10 years down the road? Did I really have to do all this? Well, maybe... but only for the warm fuzzy feeling it gives and not for any practical reason.

When I bought my Z, I searched hard to find a fairly complete car with a solid body and minimal wear and tear. I set an informal search radius of 200 miles, and spent a lot of weekends driving to look at Datsuns. Along the way I passed on a few nice looking and nice driving cars that were either patched-up (wheel openings made largely of Bondo) or where the seller was obviously misrepresenting the condition of the car (e.g. claiming original paint on an obvious re-spray).  Eventually I found a 260Z with not too much rust in the usual places, with a nice looking but not too-recent re-spray and an interior you weren't afraid to get into without a recent tetanus shot. Sure, the engine ran a bit rough, the AC didn't work and the suspension had a metal-on-metal feel, but all the pieces were there. The repairs it needed were things that bolted on.

If you read the collector car buyer guides, I did all the right things, but looking back I did something very wrong: I bought a car that you could drive but that no one really wanted to drive. Getting the car to that driver level - not just moving under its own power with the road manners of a worn out pickup truck, but feeling like an honest-to-God sports car - was a lot of work and money, where all of those there-but-nearly-worn-out parts need to be replaced anyhow. And if you don't have the money, time and facilities to get to that driver level, you are likely to end up with a neglected project car moldering in your garage.

It's too late for me, but if you're just starting down the collector car path, do yourself a favor: either buy a car that truly drives well, or if you can't get the perfection-monkey off your back start with a basket case car where you know you will have to completely replace everything. Trying to walk the middle of the road is a good way to get run over!

One day at a time

In the software engineering world there is a famous book - The Mythical Man Month by Fred Brooks - that tells of the trials and tribulations of one of the first big software projects (the development of the IBM 360 operating system).  The book has a joke that has become famous in the software biz:

Q:  "How does a  project get to be a year late?"
A:  "One day at a time!"

If you're the least bit interested in engineering you should track down a copy of the book and give it a read, but the point of this joke is that there are an endless list of minor set-backs that delay every project - a key employee has the flu, a part is delayed in shipping, a manager asks for a demonstration, the system fails in some unexpected way and requires rework - and all those tiny, impossible to predict delays simply add up.

Thats how my Datsun 260Z managed to sit unmoving in my garage for most of the last 15 years, often trapped by boxes of household junk. Every now and then I'd get it started and drive it to work or to a car show or something, but it was always a bit of an ordeal. The car didn't run well or drive well and it rattled and smelled bad inside.