CategoryUncategorised

Locost: IVA Test and Finish Line

Its been about six months since I last posted and as always I have been squirrelling away in that time. My last article, posted back in May, covered airfield testing of the car and the uncovering of a few gremlins. Lets start there.

Post-Airfield Fixes

Remember I said the engine was smoking on over-run and I was pretty sure it was the valve guides? Well I’m not always right about these things.

I wasn’t confident I could get the valve guides replaced in a short period of time so I decided to strip the cylinder head off one of my spare engines, given that’s what they are there for, and check the valve guides. If they were good and within tolerance I would give the head a quick rebuild and swap it with the one in the car.

The donor engine was out of my old daily Swift Gti and as such I knew it was in “okay” condition. It had started running a bit weird before it was pulled out of the car, but years later I would diagnosed it as either a faulty fuel pump or a jammed up fuel filter. It had started to loose power over 3500rpm and the plugs showed all the signs of being a bit lean, but generally healthy. This engine had sat in storage for about five years but actually looked pretty good on the inside. Just a bit carbon’y.

Replacement cylinder head. Dirty on the outside, clean on the inside; perfect.
Under the carbon build up this engine was as clean as you like.
That is a tea spoon of oil in each bore. Nice.

I leak tested the chambers, which were fine, and stripped apart the cylinder head . Suzuki gave a tolerance in the workshop manual for the valve guides and I had a drill-bit that was exactly the low end of their tolerance. If the drill shank fit within the guides and was tight, then they were good. Every single one of the 16 guides was a tight fit; which was fantastic.

I gave the cylinder head a good clean, re-seated the valves with course and fine cutting paste, and replaced all of the stem seals. At this point it was ready to go into the car. So I pulled the old cylinder head off the engine in the car and…

Well the picture above shows you the horror. A tea spoon oil in each cylinder. No wonder the plugs were wet! This certainly accounted for the smoke I had been seeing and meant my fix would need to be a lot more drastic. This was a huge gut punch given the amount of work I had put into rebuilding the engine, but I was done messing around and if I was going to drive the car on the road before the end of year the engine would have to get replaced.

Over a number of weekends I cleaned the donor engine and swapped over all of the important parts. The ARP head studs, dry sump system, uprated clutch etc. The old short block was out and the replacement cleaned-up version was in the car after three afternoons; I was pretty happy with this.

Cleaned up cylinder head
Replacement short block in place
Cylinder head all bolted down

With the new engine in and running it was a night and day change. A completely clean exhaust, even during warmup, and lovely clean plugs. For the first time since before 2018 I had a happy running car. This was a huge step forward and I knew that IVA was going to be possible!

Up and running!

We had a leaky clutch slave, leaky fuel tank filler, damaged rear cover and broken wheel arch bracket after airfield testing, and all of these were amended before August 2021, at which point I put the car away to sleep for a while as I was about to get married!

Pre-IVA Work

After my wedding and honeymoon I put the paperwork in for the cars IVA test (Individual Vehicle Approval) and got to my very last concerns.

My wife asked me what the car might fail on so I could prioritise and focus on a first time pass. The first thing that came to mind was noise. Back in 2017 at Snetterton the car managed 100dB at 5000rpm which was 1dB over the legal limit for IVA (99dB). I wanted to make sure the car breezed through the noise test with no issues so I decided to perform my own, as well as rebuild the exhaust back box.

The back box was some unknown carbon fibre unit I bought off of ebay many moons ago. I knew it was a from a Yamaha sports bike and appeared to be rebuildable but that was about it. I tried to remove the carbon fibre outer body and weirdly enough there was some 3mm thick aluminium underneath it! So the carbon fibre was just for looks; not my kind of think.

So, not carbon fibre than?
It had maybe 5mm of very burnt old padding inside it
Err.. no thankyou

I had to cut and peel the outer shell off to get at the internals and by this point I had already committed to completely rebuilding the whole box. Inside appeared to be a small gap for fibreglass padding, 5mm-ish all the way around, and then a series of weirdly routed baffles. The outlet didn’t even fully align with the internal piping which was quite disappointing.

I jumped on the internet and ordered a 5inch diameter piece of stainless exhaust tube, which is flared both ends to allow the old end caps to be used. I also ordered some 2inch diameter perforated stainless tube to run down the middle of the box. This was wrapped with 1.5meters of Acousta-fil exhaust material.

After a bit of welding, drilling and riveting I had a fully rebuilt back-box.

Pretty much a build your own back-box kit
Much better
Fully modified and back on the car

Using the noise meter from work we could do our own mock noise test. With the new back box installed the car managed a whisper quiet 105dB! Oops. I knew the Acousta-fil needed some time to expand and do its job, but either way I had made exhaust noise worse. That said, it sounded fantastic 🙂

How did I resolve the noise issue? I went the tried and tested route and installed a dB Killer. Not my proudest moment but they really do work. Having modified and installed this in the back-box inlet we managed 95db at 5500rpm, a full 10db reduction! That is huge. Its great to have the option to make the car more friendly if needs be.

A dB Killer baffle, with the internals switched around
Installed. I am happy that baffling is in the correct direction

Other than the odd bit of trim here and there, that was it, the car was ready for IVA.

IVA Test

Early Start and Arrival

To get to the test centre with time to spare I reckoned I needed to leave at 5am in the morning. You have to be there by 8am, with the car unloaded and ready to go, and it was an hour and half drive away from me. I understand that my maths doesn’t entirely make sense, but there was absolutely no way I was going to be late! Subsequently the traffic was amazing and I ended up sitting in the services next door beforehand, but it never hurts to be prepared!

Needless to say I got to Bristol test centre with plenty of time to spare. Although it was cold and autumnal it was quite a beautiful day, and very quiet down on the docklands.

A beautiful sky over Bristol at 7:30am
Waiting to be probed and proded

Weigh bridge

After introductions and a quick look over of the car it was straight onto the weigh bridge. The car came in at 540kg (245kg+295kg) with a full tank of fuel. This was a little disappointing as this was the heaviest I have ever seen it on the scales, although maybe this is simply the real road going weight?

It was weighed many years back in racing trim at 475kg; completely dry. Since then it has gained two full size seats with padding, a properly working water system with header and spill tank, a dry sump system with a 5 litre oil tank, a full full size fuel tank, mirrors, IVA trim, padded interior, lights, full size arches etc etc. So 540kg sounds about right! That’s the price you pay to have a proper road going car with a roll cage; I’m not going to complain.

For comparison a Mk1 MX5 weights 960kg and a Mk3 weighs 1122kg…

General build standards

The two testers had a good poke around the car before going much further just to make sure there weren’t any glaring failures or safety issues right off the bat. So far so good. They were very complimentary on the construction and there was definitely a good vibe. I felt I had presented a clean car.

While the car was on the trailer the day before I had taken the fuel cap assembly out and loctited the bolts, but I had forgotten to reattach the fuel filler cap tether! They were very forgiving and let me use my spanners to fix that issue right there and then.

Emissions

Not much to say, the 30 year old 100k+ engine flew threw with almost comically good emissions. I am glad I swapped them out!

Exterior and Interior Radii

This was the one thing that worried me the most. The radii rules are absolutely brutal. The car is tested with a fake 100mm “knee” and anything that contacts it, which is less than 5mm above a surface, must be radiused to 2.5mm. Fortunately all of my hard work, rubber trim and 3d prints really paid off! It flew through on both Exterior and Interior Radii.

There were a few questions over components I had used and we discussed what constituted a pass or a failure. It was pretty informative.

Underbody construction and alignment

After that the car went up on a hoist and was checked from underneath. It was quite cool to have someone different actually look at all the work under there. Very few, if any, people have looked at the car from that angle.

Again, they were very complimentary on the quality of the build.

Light Alignment

I had setup the light alignment using the numbers in the IVA manual and sticky tape on my garage door. My drive is not flat. That said, one of the lights was bang on and the other required a minor adjustment to pass. I was happy with that.

The equipment they use at the test centre actually shows the light pattern on the same piece of paper displayed in the IVA manual. Its pretty impressive.

Brakes and Brake Dyno

This was the first of two rolling roads that the car would go on during the day. The front and rear axles were tested separately, measuring the peak longitudinal loads they could achieve before locking, and the relevant pedal effort required to achieve those loads. This was also done at a number of increasing pedal loads to give the characteristic of the braking axles. Again, all very impressive and fun to watch.

On the rollers for the brake test

Speedo Calibration

Given you have probably already read my article covering airfield testing you know all about my method of calibrating the speedo. Guess what? It bloody worked. The car flew through the speedo test.

This is actually a really cool test as the car is put on a rolling dyno and run up to 70mph. The tester waded through the gears and the car sound great as usually. I was darn proud at this point.

Noise

Next up was the noise test. Given the dB Killer and measurements I had done beforehand I was pretty comfortable it would pass the test. It easily flew under the radar at 93ish dB. No worries there then!

One issue that did raise its ugly head is hot starts of the engine. I have been playing with the settings in Megasquirt to reduce the amount of start-up fuel put into the engine when the engine is warm but I think the firmware has a bug in it, and the temperature sensitivity doesn’t work. So it bellowed black smoke on restart for about five seconds before doing the test. Great.

Mirrors

Not much to comment on. It flew through.

Dynamic Brake Test

I have no idea what went on during this test but it sounded like the tester was enjoying himself. The intake noise was glorious.

Debrief

And that was that. Almost three years of hard work to take my little red race car from track toy to road legal car. I can’t say it didn’t have its ups and downs, especially with COVID hassling me and having a somewhat broken engine, but I am really happy with the end result.

The Locost is a weird thing. I have put so many hours into it that it kind of scares the crap out of me even when its stood still. A new phase of our relationship has begun which will hopefully be a little bit more give/take!

The final picture says it all really.

Pass! One very tired owner and one very happy car

Bonus Round: First Drive

It has taken me some time to write this article as life as been relatively busy.

All in all it took about four weeks from the IVA test to receiving my registration number. Considering the amount of flak the DVLA get they actually seemed to do everything in their power to get my registration turned around and they were really helpful on the phone.

I received my Q plate on a Friday afternoon and I had it insured and number plates the same day. This lead to me to waking up at 6:30am on the Saturday like a giddy child for my first ever drive on the road….

The early hours

What can I say? Its awesome. All of the performance numbers and pub chat aside, driving one of these cars is an experience. I imagine its much closer to riding a motorbike than it is to driving a modern hatchback. Its interactive, you feel everything. Not only that you feel like you are going warp speed when you are cruising along at 60mph. The exhaust note, the direct steering, the throttle response. Its unique.

There are certainly quicker cars. There are certainly “better” cars. But there are none like mine.

ManDoCar: Episode #5: SN15, Motorbikes, Bows, Boats and Completing a Hobby Project (Guest: Neil)

This time its not just two but three brothers having a natter.

We discuss SpaceX’s Starship SN15, running a canteen on the moon, Motorbikes, Bow making, carpentry, fixing dinghy’s and living life once a major hobby is complete. Neil is guest: he is a civil engineer, biker, archer and father of two.

ManDoCar: Episode #4: SN9 Landing Sploshion, The Cost Of Hobby Cars, Alex Buys Another Boat

A new episode of Man Do Car! Two brothers just having a natter.

We discuss the Mars Rover Landing, SpaceX Starship SN9 Landing Sploshion / SN10 Non-Sploshion, the cost of Volvo 240’s, Alex Buys Another Boat, Weird Sailing Events, the cost of Hobby Cars, Expert Rigging, Twitter Bots, curbing your enthusiasm and Electric Car Chargers.

Holiday Drag Racing, Part 2/2

Its time to simulate the big guns in drag racing; the stars of Motortrends Street Outlaws: No Prep Kings. Following on from my previous article, where I simulated my little Locost in a straight-line, I have tried my best to piece together what a No Prep car looks like on paper and what makes them able to perform a Eighth Mile Drag Race in less than 4s! Lets delve in.

“The Shocker”

The car I have loosely based my numbers on is Kye Kelley’s third generation Camaro; “The Shocker”. Kye is a top level driver and builder and is often talked about. You can read about his story here in Dragzine. Kye came second place in the 2019 championship, but it was a close call between him and Ryan Martin.

An image of Kye Kelleys third generation Camero. Taken from Dragzine.com. You can find the original article here.

Engine

The Shocker runs a Pat Musi built 959 EFI Pro Nitrous engine (959 cubic inch, 15.7 litres!). Engine Builder Magazine quotes these engines at 1,850 hp naturally aspirated and 2,800 hp on nitrous, although larger numbers are thrown around in No Prep Kings (4000hp?!?).

While no data is available to say what engine speed peak power and peak torque are made at, I have made a guess based on other engines. Rocker-arm over-head-valve V8’s are generally speed limited by their valve train and/or crankshaft so these numbers weren’t going to be far from reality. This NMCA (National Muscle Car) article suggests Pat Musi’s “smaller” engines make peak power at 7200rpm with a crank limited speed of 8000rpm.

2800hp at 7200rpm is a whopping 2769 Nm of torque. I assumed the torque curve for this engine was relatively flat, based on what I have seen on Motortrends Engine Masters. The following plot shows the guess I used in the drag simulation.

If this is hugely wrong then please feel free to get in contact with me Pat! I would love to talk to you about these amazing engines.

Chassis

The No Prep Kings rules outline a useful piece of information. A Big Block Nitrous powered car must have a base weight of 2750 lbs (1247 kg). I trust that Kye Kelley has built a car that is down at the base weight and probably requires ballast to get back up to that weight.

The third generation Camaro has a wheelbase of 2.565m (101.0 in) and the rules allow an increase in wheelbase of 3 inches, which I expect the Shocker makes use of to stabilize the car at speed.

The owners forum suggest a weight distribution of approximately 55% forward for a stock car. I can’t see this having changed too much given the bigger engine in the front and the bigger tyres in the back.

Again, I had to lean into the owners forum for drag coefficient details (not the most solid source of information) but they suggested the CdA of a third gen Camero is approximately 0.66334 (Cd: 0.340 * Area: 1.951). If we factor in an air density at sea level of 1.225 kg/m^2 we get an overall pCdA of 0.813. The Locost was suggested to be around 0.9, which suggests the Camero gets a large amount of its drag from being a much bigger car; always worth thinking about when trying to reduce this number.

Drivetrain

I couldn’t find what gearbox is currently in The Shocker, so I looked to Ryan Martins car; the winner of season 3. He runs a TH400 automatic three speed transmission. The ratios of which are listed on the internet.

I have made one massive oversight: this car is an automatic. The engine speed to road speed is not directly coupled through a clutch, it slips due to being coupled through a torque converter. This allows the engine to stay around peak torque longer without having to drop down the torque curve, but it is less efficient. I am going to assume the difference is negligible for the sake of simplicity.

Tyres

Again, I had to turn to Ryan Martins car for additional information. His chassis is setup to run “Outlaw 10.5/Radial” rear tyres which are, as you guessed it, 10.5 inchs wide. The Mickey Thompson 29.5/10.5-15W is a pretty good example of this (I think!) and they stand at 29.6inches diameter.

Completely Guessed Variables

I had to have a guess at four variables: the height of the center of gravity, the effective Tyre Grip/Fricton, the Shift Delay time and the Final Drive Ratio. My selected numbers and the reasonings behind them were as follows:

Height of center of gravity

I have stuck with 0.4m. These drag cars run very low ride heights by the looks of things. In reality its probably higher, given the increased rearward weight transfer that having a higher COG would give you and the subsequent added benefit to traction. That said, I believe the tyres are so grippy in these No Prep cars that at launch all the weight is on the rear tyres anyway; that’s that.

Tyre Grip

This SAE paper (The Magic of the Drag Tire) quotes top fuel dragsters and funny cars accelerating at over 4g’s. While the actual coefficient of friction of the tyre is lower than 4.0 the effective friction is around 4.0 due to the way energy is stored in the tyre and the way it interacts with the rubbered surface.

I figure a cheaper, smaller, off the shelf tyre isn’t as “grippy” and given the surface is not prepared, the overall coefficient of friction is in the 2 – 3 region. Its a guess, but as you’ll see later its not bad.

Shift Delay

The gearbox is shifted automatically which makes the whole question of “shift delay” a little hard to workout as the engine never clutches. I have thrown in a value of 0.1s as a guess.

Final Drive Ratio

I adjusted this number to give close to max engine speed at the end of the track. In the end I settled on a 3:1 ratio.

Summary of Key Variables

VariableValueUnitNote
Total Mass1247kgBase weight from the No Prep Kings rules
Weight Distribution Forward55%Stock Camaro
Height of the Centre of Gravity0.4mGuess
Wheelbase2.6412m104in
Drag Coefficient (pCdA)0.813Taken from the Camaro owners forum
Rear Axle Grip3N/NVery sticky drag tyres in a rubbered launch box
1st Gear Ratio2.48:1TH400 Automatic Transmission
2nd Gear Ratio1.48:1
3rd Gear Ratio1.00:1
Final Drive Ratio3:1Guess. Tuned to the simulation.
Wheel Diameter0.75184m29.6 inches
Wheel Circumference2.3620mThe diameter multiplied by pi

A 3.9s Pass

The research above allowed me to produce the following straight-line simulation.

Well there you have it, the eighth mile in 3.94s @ 202.5mph and 0-60mph in 0.915s. Quicker than the Locost? Most definitely!

Note that the car is entirely traction/grip limited throughout first gear, but beyond that point it is flat out down the track. I don’t expect this is always the case. The grip in the start box will be much higher, due to the rubber that is laid down from burnouts. I expect grip drops off quickly the further down the track the car travels. You would want to tune your gears and power wisely based on the track you are racing on and the surface, which is what you witness the drivers doing on the show.

Final Thoughts

I really enjoyed doing the research for this article. It took a lot of digging around drag racing websites and parts stores to understand what is underneath a No Prep car.

I’m tempted to have a crack at Dirt Track Racing next. Perhaps investigating what it takes to drive fast sideways? We’ll soon see.

I hope you enjoyed the content!

Code (Octave GNU or Matlab)

clear all; close all; clc;

# Vehicle Definition
mass = 1247;       # [kg], Total Vehicle Mass, From the No Prep Kings rules
wd = 0.55;        # [-], Forward Weight Distribution, Stock Camero
h_cog = 0.4;      # [m], Height of COG, Guess
wheelbase = 2.565 + (25.4*3)*0.001;  # [m], Wheelbase, From Wikipedia
drag_pCdA = 0.813;   # [], Drag Coefficient * Area * Air Density, taken from the Camero forums
grip = 3;       # [N/N], Rear Axle Peak Grip, Guess based on 4g launch of proper drag cars

# Pat Musi 959 on Nitrous
engine_speed = [0,2000,4000,6000,7200,8000]; # [rpm]
engine_torque = [2000,2750,3000,3000,2769,2450]; # [Nm]

# Plot for Engine Power / Torque
if 0
  figure; hold on; grid on;
    plot( engine_speed, engine_torque, 'b' );
    plot( engine_speed, engine_torque .* (2*pi*engine_speed/60) * 0.001 * (1/0.7457), 'r' ); # [hp], Metric
    h = legend( 'Engine Torque [Nm]', 'Engine Power [hp]' );
    legend (h, "location", "northeastoutside");
    xlabel( "Engine Speed [rpm]" );
    title( "My guess at an impressive Pat Musi 959 Nitrous V8" );
    return;
endif

gear_ratios = [2.48, 1.48, 1.00]; # TH400 automatic transmission
gear_ratios_max = 3;
gear_final_drive = 3; # Guess based on max RPM at the end of the track
gear_wheel_diameter = (29.6*25.4) * 0.001; # [m], Mickey Thompson 29.5/10.5-15W
gear_wheel_circumference = gear_wheel_diameter * pi; # diameter * pi
gear_shift_rpm = [8000, 8000, 8000]; # As limited by the Engine
gear_shift_time = [0, 0.1, 0.1];

# Calculate max possible speed
v_max = ( gear_wheel_circumference * gear_shift_rpm(gear_ratios_max) ) / ( gear_ratios(gear_ratios_max) * gear_final_drive * 60 );

# Simulation Variables
g = 9.81;         # Gravity
t = 0;            # [s], Current Time
dt = 0.001;       # [ds], Delta Time
a = 0;            # [m/s^2], Instantaneous Acceleration
v = 0;            # [m/s], Instantaneous Velocity
s = 0;            # [m], Distance Travelled
gear = 1;
zero_to_sixty_time = 0;
gear_shift_timer = 0;

# Datalog
t_log = [];
a_log = [];
v_log = [];
s_log = [];
rpm_log = [];
throttle_log = [];

# 1/4 Mile = 402.336 meters
# 1/8 Mile = 201.168
while s <= 201.168
  
  # Calculate the rotational speed of the rear axle [hz]
  axle_speed = v / gear_wheel_circumference;
  
  # Calculate engine rpm based on current speed
  rpm = gear_ratios(gear) * axle_speed * gear_final_drive * 60;

  # Should we up shift?
  if gear < gear_ratios_max
    if rpm > gear_shift_rpm(gear)
      gear = gear + 1;
      gear_shift_timer = gear_shift_time(gear);
    endif
  endif
  
  # Calculate the weight on the rear axle (including weight transfer)
  # and the maximum force the tyre can supply
  mass_rear = mass*(1-wd) + (mass * a * h_cog / wheelbase); # [kg]
  if mass_rear > mass
    mass_rear = mass;
  endif
  max_tyre_force_rear = mass_rear * grip * g; # [N]
  
  # Limit engine torque lookup within engine max rpm
  if rpm > gear_shift_rpm(gear)
    engine_torque_output = interp1 ( engine_speed, engine_torque, gear_shift_rpm(gear) );
  else
    engine_torque_output = interp1 ( engine_speed, engine_torque, rpm );
  endif
  engine_torque_at_axle = engine_torque_output * gear_ratios(gear) * gear_final_drive;
  engine_force = 2 * engine_torque_at_axle / gear_wheel_diameter;
  
  # Calculate drag
  drag_force = 0.5 * drag_pCdA * v * v; # [N]
  
  # Estimate throttle position
  throttle = 1;
  if engine_force > max_tyre_force_rear
    throttle = max_tyre_force_rear / engine_force;
  endif
  
  # Are we shifting gears?
  if gear_shift_timer > 0
    max_tyre_force_rear = 0;
    engine_force = 0;
    throttle = 0;
    gear_shift_timer -= dt;
  endif
  
  # Calculate Acceleration
  a = ( min(max_tyre_force_rear, engine_force) - drag_force) / mass;
  
  # Limit maximum speed, essentially a rev limiter
  if v >= v_max
    if a > 0
      a = 0;
    endif
  endif
  
  # Rough Integration
  v = v + a*dt;
  s = s + v*dt;
  t = t + dt;
  
  # Add to the Datalog
  t_log = [t_log; t];
  a_log = [a_log; a];
  v_log = [v_log; v];
  s_log = [s_log; s];
  rpm_log = [rpm_log; rpm];
  throttle_log = [throttle_log; throttle];
  
  # Grab 0-60 time
  if zero_to_sixty_time == 0
    if v .* 2.23694 >= 60
      zero_to_sixty_time = t;
    endif
  endif
  
endwhile

figure;
subplot(5,1,[1 2]); hold on; grid on;
  plot( t_log, v_log .* 2.23694, 'b' ); # [mph]
  ylabel( "Speed [mph]" );
  title( [num2str(t) "s Eighth Mile @ " num2str(v .* 2.23694, 4) "mph, 0-60mph in " num2str(zero_to_sixty_time) "s"] );
subplot(5,1,3); hold on; grid on;
  plot( t_log, a_log ./ g, 'r' ); # [g]
  ylabel( "Acceleration [g]" );
subplot(5,1,4); hold on; grid on;
  plot( t_log, rpm_log, 'k' );
  ylabel( "Engine Speed [rpm]" );
subplot(5,1,5); hold on; grid on;
  plot( t_log, throttle_log  .* 100, 'k' );
  xlabel( "Time [s]" );
  ylabel( "Throttle [%]" );
  ylim( [0 100] );
set( gcf, 'position', [300, 202, 560, 755] );


Holiday Drag Racing, Part 1/2

COVID19, and the isolation associated with it, has made us all go a little mad. Personally, I am in need of some Automotive escapism, and my choice of holiday TV has been Street Outlaws No Prep Kings (Season #3, you can find it on MotorTrend).

While drag racing is considered very niche in the UK, it’s huge over the pond and there are loads of online shows covering it. No Prep Kings pits big high powered American cars against each other in eighth mile drag races. Each round the losers are knocked out until there is only one winner left. With approximately 32 cars competing in each event, and with some serious personalities knocking around the pits, it’s properly entertaining.

I’ll be honest with you, I often skip the preamble and go straight to the racing, so lets do that right now!

Straight-line Simulation

To my British audience: Don’t write-off Drag Racing just yet. Yes they only go in a straight-line, but there is a lot more involved in proper drag racing than it may first appear and the cars are not trivial to build or tune. That said, I don’t own a drag car. I own a British Sports Car, and that is going to be our reference point.

I have thrown together a very quick and dirty simulation to get things going; the code is attached at the end of the article. It’s rough. Really rough, so to all the Engineers out there: this is a tool to show how interesting drag racing is, not a Curriculum Vitae. The results also yield insights into how to go fast in a straight-line, which I think is worthwhile.

A simulation isn’t worth much without some input data, so to begin with we I used some rough estimates of the key variables of my little Locost.

Chassis

VariableValueUnitNote
Total Mass600kgAbout right. It was measured at 490kg back in 2014 before receiving its road gear and dry sump. Then add my weight and some fuel…
Weight Distribution Forward43%Again, measured back in 2014 and I doubt it has changed much since.
Height of the Centre of Gravity0.4mI have guesstimated a number well above the crank centre line of the engine and slightly above the top of the chassis. If anything, it’s probably lower in reality
Wheelbase2.35mMeasured in CAD and confirmed with a tape measure
Drag Coefficient (pCdA)0.9I had to get a reference for this from an American Locost forum, but I do know this number is “high” which is correct for a Seven; they are very high drag cars. Note that this number includes air density, which simplifies the drag equation
Rear Axle Grip1.2N/NOkay, stick with me here. I reckon this is the grip level of a decent touring car tyre at a reasonable weight and pressure. But we’ll soon find it doesn’t matter that much to begin with.

Engine

I had to have a guess at an engine torque curve given that I am yet to have a successful dyno run. The stock G13B is said to make 110Nm at 5500rpm and 100hp at 6500rpm. My quick maths suggests a torque of 109.5Nm at 6500rpm (torque=power/speed). That’s only two data points! To round things off I set the zero speed torque as 90Nm and the roll off torque at 8000rpm to 80Nm; this is probably optimistic but it will do for now. The curve was as follows:

To begin with the engine shifts at 6500rpm (peak power).

Drivetrain

The following gear ratios are from the early model Suzuki Samurai gearbox that is in the Locost. I confirmed these ratios to be correct using engine speed and wheel speed calculations (they can also be found here).

VariableValueUnitNote
1st Gear Ratio3.652:1Terribly short ratio
2nd Gear Ratio1.947:1
3rd Gear Ratio1.423:1
4th Gear Ratio1:1Not unusual
5th Gear Ratio0.795:1This is the early Suzuki Samurai gearbox. A slightly shorter ratio is available in the later boxes
Final Drive Ratio4.3:1MX5 Mk1 Differential. The only ratio available I believe.
Wheel Diameter0.5522mBased on a 185mm wide 60 profile tyre on a 13inch rim
Wheel Circumference1.7348mThe diameter multiplied by pi

Anyone that knows anything about gearboxes can spot that these ratios aren’t great. The first is way too short and the fifth is way too long. But, I am hoping through a little simulation, we can work out some strategies to live with what we have.

Our First Pass

With all that committed to code and the use of a really simple linear integrator we get a quarter mile pass that looks something like this:

A 13.463s quarter mile, going from 0-60mph in 4.495s? Not bad for a little 1.3 litre sportscar. Sadly though, there are a number of assumptions in this simulation that may make this massively unrealistic:

  • Instant weight transfer. There are no real chassis dynamics in this simulation.
  • A completely locked rear differential. Okay this is not as weird an assumption as you might think. I now run a locking differential which should hopefully, under hard launch conditions, be locked.
  • The grip is relatively high. The throttle is pegged at 100% the whole time. But I’ll be honest with you, this is the case for the Locost on warm tyres and a good surface. Its not got acres of power so you don’t need to pedal it.
  • A perfect launch. There is no holding the revs and trimming the clutch here.
  • No gearshift times. This is one thing I just can’t stand for. In the above pass there are four gearshifts that all take place instantaneously. The time these actually take could have had potentially a huge effect on the outcome of the simulation time.

Adding a Gearshift Delay

With a manual synchronised transmission you waste time clutching the engine/gearbox when selecting a new gear. During this time period you are not accelerating forward; in fact you are slowing down due to drag.

From my own data I know that a gearshift can take anything between 0.5s to 1.0s to complete, depending on how aggressive I am being on the gearbox. I added this into the simulation as a time period after any shift where no engine power is used.

The updated simulation looked like this:

Well. That’s sucks.

Adding a gearshift delay into the simulation of 1.0s cost a total of 1.664s in the quarter mile and 2.125s in 0-60mph time. I’d rather have that performance back thankyou! Here is a table giving a sweep of the results:

Run [#]Gearshift Delay [s]Quarter Mile [s]Delta [s]Speed [mph]Delta [mph]0-60mph [s]Delta [s]
10.013.463-98.58-4.495-
20.514.3050.84296.37-2.215.5581.063
31.015.1271.66493.35-5.236.6202.125

So what options do we have to get this performance back? We could simply reduce the shift time (automated paddleshift anyone?) but that isn’t a realistic option for the time being.

How about making better use of the torque that we already have? If you look at the acceleration plot its clear that the car is still accelerating at 6500rpm. While it continues to accelerate hard, and the engine can take the extra rpm reliably, its worth delaying the gearshift.

Lets sweep the shift rpm and see what difference it makes, keeping the 1.0s shift delay in the simulation for realism.

Engine Speed

The results of the simulations were as follows:

Run [#]Engine Shift Speed [rpm]Quarter Mile [s]Delta [s]Speed [mph]Delta [mph]0-60mph [s]Delta [s]
1650015.127-93.35-6.620-
2700014.795-0.33294.040.696.425-0.195
3750014.529-0.59894.401.056.287-0.333
4800014.327-0.894.190.845.068-1.552

Well that’s mighty interesting! Shifting at a later RPM yielded a benefit in every case, and in the final simulation saw a full 1.219s improvement in 0-60mph time. But why might this be? Plotting each run against each other makes the differences quite clear.

Note that the following plot uses distance as the x-axis, as opposed to time. I find this makes comparison much easier.

Well there you have it, shifting at 8000rpm means you are only changing gears only once before 60mph; hence the big improvement in this metric. This kind of suggests that 0-60 times are a little redundant and are very dependant on gear ratios and shift points. That said, it did go faster!

Also note that even though peak horsepower was at 6500rpm, shifting at 8000rpm was faster in a straight-line. This means that the shape of the torque curve beyond peak power is important, and dictates the most efficient shift point. Keep that in mind when mapping an engine.

Obviously my current torque curve is a complete guess so it may not actually be beneficial to shift at this rpm in the Locost, but its worth considering.

Power and Gear Ratios

Up to this point the very short first gear ratio hadn’t caused any problems. The throttle is always pegged at 100% throughout the whole run when not shifting gears. However, what if we add more power?

The Cultus Spec G13B

In my recent engine rebuild I used Suzuki Cultus Cams and Pistons. This raised the cam lift from 7.5mm to 8mm and the compression from 10:1 to 11.5:1. These parts were only available in Japan and are relatively rare, but raise the peak horsepower from 100hp to 114hp. I believe peak horsepower is moved from 6500rpm to 7250rpm, but I can’t remember where I read this; details on these engines are hard to find in anything but Japanese.

I assumed the details above were correct and made a modified torque curve to suit:

To create the above I shifted all of the data points by 725rpm and then multiplied the entire torque curve by 104%. This gives the desired 114hp at 7250rpm.

Engine Comparison

Using the same simulation as before, with 8000rpm shift points for the original engine and 8725rpm shift points for the new engine, I could make a comparison. The results were as follows:

Run [#]EngineQuarter Mile [s]Delta [s]Speed [mph]Delta [mph]0-60mph [s]Delta [s]
1Stock G13B14.327-94.19-5.068-
2JDM Cultus Cams and Pistons13.74-0.58796.942.754.712-0.356

Well that’s a bit more like it. Much closer to the original numbers without gearshift delays and considerably quicker in a straight-line.

Note however that the car is still not traction limited. If this is truly the case in real life than this first gear ratio is not the end of world at this power level. That said, I was still interested in what changes in first gear ratio would make.

Different First Gear Ratios

A scan of first gear ratios yielded the following comparison. I made use of the new engine data above as a baseline setup.

Run [#]1st Gear RatioQuarter Mile [s]Delta [s]Speed [mph]Delta [mph]0-60mph [s]Delta [s]
1Original 3.652:113.740-96.94-4.712-
23.000:113.8420.10296.7-0.244.8840.172
32.500:114.0910.35196.13-0.815.2940.582

And… it went slower. My thought is a longer first gear is only needed if you are traction limited in 1st gear. That means if you have more power or lower grip, its worth changing. Other than that, short is fast… as long as you have a relatively flat torque curve and the drop off in torque on the upshift isn’t bad.

Plenty to discuss, but this is not the space to go in depth.

Drag Sensitivity

I was interest in what effect decreasing drag would have on quarter mile time. My little Lotus 7 is pretty quick from 0-60mph but runs out of steam somewhere beyond that point due to the large drag coefficient is has.

I can vouch that the original Suzuki Swift GTi that its G13B engine came out of could do 125mph in a straight-line, but the Locost tops out at just over 100mph. That’s a huge difference in drag.

The results from the drag scan were as follows:

Run [#]Drag [-]Quarter Mile [s]Delta [s]Speed [mph]Delta [mph]0-60mph [s]Delta [s]
1Original13.740-96.94-4.712-
2-5%13.712-0.02897.610.674.703-0.009
3-10%13.684-0.05698.291.354.694-0.018

The results were quite interesting as I expected the drag to have a far greater effect than it did. There appears to be a clear change in the shift point between third and fourth gears, but this is almost 75% of the way down the track, so the overall difference in quarter mile time is minor.

Interestingly, when I was driving around Snetterton I spent most of my time in 3rd and 4th gears, where the data above suggests drag has a notable effect.

Grip Sensitivity

Lastly, before I venture into the world of 1/8th mile monsters, I wanted to simulate the Locost on a less than perfect surface or tyres.

Autosolo events have to start with dead cold tyres, no warming is allowed, and the surface often starts the day covered in stones and debris. This means the first few starts are always worse than those later in the day; this is due to low grip.

The results from the grip scan were as follows:

(Appologese for the lack of legend, I have been fighting Octave on this front! Baseline is Black, -15% Grip is Blue, -30% Grip is Red)
Run [#]Grip [%]Quarter Mile [s]Delta [s]Speed [mph]Delta [mph]0-60mph [s]Delta [s]
1Original13.740-96.94-4.712-
2-15%13.7670.02796.91-0.034.7490.037
3-30%13.9970.25796.72-0.225.0330.321

Lower grip, slower car; not a surprise. That said, such a little lightweight car with low power wasn’t as much effected by lower grip than I expected.

Summary

On a good day with warm tyres the Locost in its current trim can potentially do a 13.74s Quarter Mile @ 96.94mph, with a 0-60mph of 4.712s. One of the lowest hanging fruits is shift times (I knew this!) to make the car quicker in a straight-line.

What I didn’t tell you is that this is equivalent to an Eighth Mile time of 8.772s @ 82.43mph. No Prep Drag Cars can do this in as little 3.900s!

In the second part I will play with the numbers and see what is required to a get a car to travel this distance in a much shorter time.

Code (Octave GNU or Matlab)

clear all; close all; clc;

# Vehicle Definition
mass = 600;       # [kg], Total Vehicle Mass
wd = 0.43;        # [-], Forward Weight Distribution
h_cog = 0.4;      # [m], Height of COG
wheelbase = 2.35;  # [m], Wheelbase, A guesstimate from the CAD, it changes with castor
drag_pCdA = 0.9;   # [], Drag Coefficient * Area * Air Density
# Taken From: http://www.usa7s.net/vb/showthread.php?9876-Caterham-Wind-Tunnel-Testing
# Approximately 1.5 * 0.66, which is inline with what others are quoting
# I trimmed this down by 15% inline with observations at Snetterton
grip = 1.2;       # [N/N], Rear Axle Peak Grip

engine_speed = [0,5500,6500,8000]; # [rpm]
engine_torque = [90,110,109.5,80]; # [Nm]

# Plot for Engine Power / Torque
if 0
  figure; hold on; grid on;
    plot( engine_speed, engine_torque, 'b' );
    plot( engine_speed, engine_torque .* (2*pi*engine_speed/60) * 0.001, 'r' ); # [kW]
    plot( engine_speed, engine_torque .* (2*pi*engine_speed/60) * 0.001 * (1/0.7457), 'r' ); # [hp], Metric
    h = legend( 'Engine Torque [Nm]', 'Engine Power [hp]' );
    legend (h, "location", "northeastoutside");
    xlabel( "Engine Speed [rpm]" );
endif

gear_ratios = [3.652, 1.947, 1.423, 1, 0.795];
# From: http://www.zukioffroad.com/tech/suzuki-samurai-specifications/
gear_ratios_max = 5;
gear_final_drive = 4.3;
gear_wheel_diameter = (185*0.60*2 + 13*25.4) * 0.001; # [m]
gear_wheel_circumference = gear_wheel_diameter * pi; # diameter * pi
gear_shift_rpm = [6500, 6500, 6500, 6500, 6500];
gear_shift_time = [0, 1, 1, 1, 1];

# Simulation Variables
g = 9.81;         # Gravity
t = 0;            # [s], Current Time
dt = 0.001;       # [ds], Delta Time
a = 0;            # [m/s^2], Instantaneous Acceleration
v = 0;            # [m/s], Instantaneous Velocity
s = 0;            # [m], Distance Travelled
gear = 1;
zero_to_sixty_time = 0;
gear_shift_timer = 0;

# Datalog
t_log = [];
a_log = [];
v_log = [];
s_log = [];
rpm_log = [];
throttle_log = [];

# 1/4 Mile = 402.336 meters
# 1/8 Mile = 201.168
while s <= 402.336
  
  axle_speed = v / gear_wheel_circumference;
  
  # Calculate engine rpm based on current speed
  rpm = gear_ratios(gear) * axle_speed * gear_final_drive * 60;
  
  # Should we up shift?
  if gear < gear_ratios_max
    if rpm > gear_shift_rpm(gear)
      gear = gear + 1;
      gear_shift_timer = gear_shift_time(gear);
    endif
  endif
  
  # Calculate the weight on the rear axle (including weight transfer)
  # and the maximum force the tyre can supply
  mass_rear = mass*(1-wd) + (mass * a * h_cog / wheelbase); # [kg]
  if mass_rear > mass
    mass_rear = mass;
  endif
  max_tyre_force_rear = mass_rear * grip * g; # [N]
  
  if rpm > gear_shift_rpm(gear)
    engine_torque_output = interp1 ( engine_speed, engine_torque, gear_shift_rpm(gear) );
  else
    engine_torque_output = interp1 ( engine_speed, engine_torque, rpm );
  endif

  engine_torque_at_axle = engine_torque_output * gear_ratios(gear) * gear_final_drive;
  engine_force = 2 * engine_torque_at_axle / gear_wheel_diameter;
  
  # Calculate drag
  drag_force = 0.5 * drag_pCdA * v * v; # [N]
  
  # Estimate throttle position
  throttle = 1;
  if engine_force > max_tyre_force_rear
    throttle = max_tyre_force_rear / engine_force;
  endif
  
  # Are we shifting gears?
  if gear_shift_timer > 0
    max_tyre_force_rear = 0;
    engine_force = 0;
    throttle = 0;
    gear_shift_timer -= dt;
  endif
  
  # Calculate Acceleration
  a = ( min(max_tyre_force_rear, engine_force) - drag_force) / mass;
  
  # Rough Integration
  v = v + a*dt;
  s = s + v*dt;
  t = t + dt;
  
  # Add to the Datalog
  t_log = [t_log; t];
  a_log = [a_log; a];
  v_log = [v_log; v];
  s_log = [s_log; s];
  rpm_log = [rpm_log; rpm];
  throttle_log = [throttle_log; throttle];
  
  # Grab 0-60 time
  if zero_to_sixty_time == 0
    if v .* 2.23694 >= 60
      zero_to_sixty_time = t;
    endif
  endif
  
endwhile

figure;
subplot(5,1,[1 2]); hold on; grid on;
  plot( t_log, v_log .* 2.23694, 'b' ); # [mph]
  ylabel( "Speed [mph]" );
  title( [num2str(t) "s Quarter Mile @ " num2str(v .* 2.23694, 4) "mph, 0-60mph in " num2str(zero_to_sixty_time) "s"] );
subplot(5,1,3); hold on; grid on;
  plot( t_log, a_log ./ g, 'r' ); # [g]
  ylabel( "Acceleration [g]" );
subplot(5,1,4); hold on; grid on;
  plot( t_log, rpm_log, 'k' );
  ylabel( "Engine Speed [rpm]" );
subplot(5,1,5); hold on; grid on;
  plot( t_log, throttle_log  .* 100, 'k' );
  xlabel( "Time [s]" );
  ylabel( "Throttle [%]" );
  ylim( [0 100] );
set( gcf, 'position', [300, 202, 560, 755] );

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