It happened again. Alex and I got behind our microphones and discussed the state of our hobby projects and many other random pieces of Engineering.
Dinghy updates, paint types, the magic of radio 4, man do compressors, compressed air cars, the Nissan leaf, electric car ownership, tesla’s, drag simulation, smugly pre-heating your car, the Locost’s shiny bodywork and the label “sports car”
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!
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.
About 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 Forward
Again, measured back in 2014 and I doubt it has changed much since.
Height of the Centre of Gravity
I 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
Measured in CAD and confirmed with a tape measure
Drag Coefficient (pCdA)
I 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 Grip
Okay, 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.
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).
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).
1st Gear Ratio
Terribly short ratio
2nd Gear Ratio
3rd Gear Ratio
4th Gear Ratio
5th Gear Ratio
This is the early Suzuki Samurai gearbox. A slightly shorter ratio is available in the later boxes
Final Drive Ratio
MX5 Mk1 Differential. The only ratio available I believe.
Based on a 185mm wide 60 profile tyre on a 13inch rim
The 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:
Gearshift Delay [s]
Quarter Mile [s]
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.
The results of the simulations were as follows:
Engine Shift Speed [rpm]
Quarter Mile [s]
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.
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:
Quarter Mile [s]
JDM Cultus Cams and Pistons
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.
1st Gear Ratio
Quarter Mile [s]
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.
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:
Quarter Mile [s]
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.
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:
Quarter Mile [s]
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.
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
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]" );
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;
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);
# 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;
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) );
engine_torque_output = interp1 ( engine_speed, engine_torque, rpm );
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;
# Are we shifting gears?
if gear_shift_timer > 0
max_tyre_force_rear = 0;
engine_force = 0;
throttle = 0;
gear_shift_timer -= dt;
# 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;
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] );
I couldn’t bring myself to write a full article on how the car is getting on, so I decided to do something a little different: a podcast! Enjoy. All the relevant pictures are below as well as dingy chat!
We discuss painting, IVA preparation, driving at Snetterton, engineering learning, SpaceX hydraulic systems, faulty brake callipers, peak performance, why limited slip differentials rock, the Hoonigan donk, exhaust wrap, and lastly, engineering in a pandemic.
Nothing quite gets the internet clickidy-clicks like a 3D printing article! In the following post I use 3D printing to fix something that wasn’t really broken.
The OLD Design
I have never been happy with the original mountings for the inlet trumpets on the Locost. Its quite common to use silicone hose to align everything within a retro-fit throttle body system and sadly mine was no different. This design can lead to miss-alignment between the trumpets and the throttles, potential shrouding of the inlet path and variations in inlet length; cylinder to cylinder.
This is the kind of stuff that keeps me up at night and it needed to be improved.
The original setup used a nice carbon fiber backing plate to mount the airfilter too. This was as soft as a chocolate tea pot, and four aluminum trumpets were glued-in with black polyurethane sealant. It never failed, it was light and did its job okay; but it wasn’t perfect.
I wanted a new design that would allow me to interchange different length trumpets, for testing on the dyno, and ensure the trumpets would inline with the inlet tract. So I turned to CAD to see what I could conjure up…
The NEW Design
Engine tuning is highly sensitive to inlet path length (read one of the best articles in the world if you want to know more), and I wanted to ensure that this variable remained static/constant. This being the case, It was important that the aluminium inlet trumpets were held up tight to the throttle bodies and positioned concentrically.
I started by measuring the GSXR throttle bodies that currently sit on the engine and then 3D printed some prototypes. The first design to nail down was the backing plate mounts. These would make the transition from the round throttle bodied to the flat air filter backing plate and essentially hold the whole lot to the engine.
I settled on a design that pushed onto the throttle bodies and over a useful cast-in ridge. This then clamped down with a jubilee clip. As a rule of thumb, jubilee clips aren’t super sexy, but when combined with dark grey plastic parts they can look utilitarian and purposeful.
I did try a version that held on using the friction supplied by an M4 bolts. This was a terrible idea. Plastic parts are not strong in tension and it would simply bend the mount when being tightened down.
The final design looked like this.
From here I had a nice flat surface to work. I carried across the jubilee clip compression-based design over to the trumpet side, as it worked so well on the throttle body side. This also allows quick release of the trumpets for switching to different lengths.
Its hard to see in the following CAD drawing, but the whole lot is sealed together with rubber nitrile o-rings. There is an o-ring between the backing plate and the throttle body mount, and an o-ring between the throttle body mount and the throttle body itself. These are super easy to design in, reusable and reliable.
Then is was simply a case of printing out eight the separate parts and cutting out the backing plate. The inner prints took approximately 3hrs each to make and the outer 2hrs each.
As always, hit go and come back later. These were made is standard PLA and, as they are on the cold side of the engine, I have no qualms about it.
The whole lot was finished off with some pretty aluminium mounting bolts for the air filter.
This setup is definitely heavier than the previous, but its far more stout and should allow for some fun experimentation on the dyno.
I have been considering building a dry sump for a long time, in fact, ever since I started building the the car. However they are a fairly complicated piece of kit, and I have therefore shied away from them until now. Fortunately I changed my mind due to the data I collected at Snetterton and having access to a decent Turret Mill at my new job. Lets get into this.
What is a Dry Sump?
Up until now I have run a Wet Sump on the Locost. In a Wet Sump system oil passes down into the oil pan under gravity and is fed back into the oil pump via a static pickup. Under longitudinal and lateral acceleration this pickup can become uncovered, leading to oil starvation and heartbreak.
A Dry Sump deals with this problem by running an extra pump attached to the engine; a Vacuum Pump. This moves oil from the sump pan to an external tank, which is tall and thin, and much less susceptible to oil starvation. An external oil pump, or the original internal pump, is then fed from this tank; supplying oil to the engines bearings and moving parts.
Although I have built a complicated baffled and gated Wet Sump the car still experiences a slow drop off in oil pressure in long right hand corners. I felt it was finally time to take the leap and fix this once and for all with a Dry Sump System.
If you still have no idea what I am on about, my previous post covering the build of my Wet Sump is a good place to start (link).
What are the Benefits?
Depending on the oil tank used, it allows constant cornering at a lateral acceleration of up to 5g.
Instead of the crank case being under positive pressure, due to combustion blow by, it can be designed to be under constant vacuum. This helps to…
Reduce Windage, increasing engine efficiency at high speeds.
Improve the in-cylinder octane level, as less oil passes by the rings into the combustion chamber.
As a Design Engineer I’m trying to do more… Design, when it comes to the Locost. So instead of jumping straight in and cutting metal on day #1, I drew up what the system was going to look like and got an idea of the layout. Packaging in the Locost is TIGHT, so this wasn’t ever going to be easy.
This is the space I had to work with. The ignition trigger wheel was already there and potentially in the way, and there wasn’t enough room to fit a pump on the passenger side of the bay (the alternator was in the way!) and the pump needed to be positioned to avoid the chassis rail and steering column. Oh, and retain a place for the ignition trigger sensor…
This was my initial design. I already had a Pace CD2000 Pump that I had bought many moons ago for such an occasion and I modified it into a two-stage vacuum pump, with no pressure stage. I then used some calipers to measure and get it into cad. This allowed me put a drive gear on the front of the “engine” (well sump flange and front pulley) and work out the beginnings of the new oil pan.
After many evenings and iterations it looked something like above. I had decided to use silicone hose for the oil routing between the sump and pump, as it gave many more options in terms of packaging. This mean’t I had to run steel tubing out of the pan.
I then finalised the design of the drive-hub and gear. It indexes onto the lower cam-drive and is driven through the five M6 bolts that hold onto the front pulley.
With the component designs sorted I could finally start cutting steel. I had a spare standard sump on one of my engines, so I used that as a donor flange. When I built the baffled sump I made my own flange and… it wasn’t as good as the pressed Suzuki item. All the small details really help to seal the gasket to the block and I was happy to carry them over. I marked the sump 25mm down from the flange and attacked it with the grinder.
At this point I got my own lathe to help move the project along; achieving a massive life goal in the process! Its only a little Sieg SC3, but it is super useful for making little top hats and smallish components. The drive hub for example.
I was able to go from bar-stock to component in one afternoon. I had made my own digital read out for the top slide which made boring accurate depths super easy.
The final features were then machined on the mill. A slot to clear the crank keyway, the five M6 bolt holes and the five M4 gear mounting threads.
This was what I thought would be the hardest part of the project, but once I used the right equipment to make the components it was actually really straightforward.
At this point I could properly place the vacuum pump in the real world, choose a belt length, and finish the oil-pan.
What I don’t have is pictures of the countless hours I spent trying to seal the sump for leaks. I used water and air to find pin-holes and just kept welding, grinding, checking and repeating. Side note: I need to get a TIG welder…
I also added some bolt-in mesh within the sump to protect the outlets. You’ll noticed that I ended up moving one of the oil outlets relative to the CAD. It actually ended up far tighter and better packaged in real life.
Having made the oil-pan, pump-mount and drive, there were a few small components that needed to be made before I could install the pan. One of these was a bung for the original oil pickup in the engine. This was essentially a large top hat, bolted in place, allowing the use of the original pickup seal.
Following this I could finally install the whole lot in the car.
In the final part I will cover the installation of the oil tank and oil lines, and then find out if it actually works!