CategoryLocost

Locost: Fixing the handling

I have been really looking forward to this phase of Locost ownership: the development! With the car on the road I can now make changes and feel the difference in the engine and the handling almost straightaway. Back in my previous job I used to do this in a high tech racecar simulator, but I felt the real learning would always be on the road in my own car. Here goes!

Super scary to drive

I have put approximately 100 miles on the Locost since it first hit the road. These have been spirited drives to get to know the handling and deal with any reliability issues, as well as a few commutes to work. In short: I have been dodging winter showers.

The car has been really struggling with poor straight-line stability. Once its in a corner it feel “okay” but in a straight-line it would dart in and out of bumps, and generally wonder across the road, even though I was holding the steering dead straight. This has been really hindering my enjoyment and generally slowing me down. I can’t push the car without holding on to the steering wheel for dear life, which doesn’t seem entirely right!

With this in mind I put the car up on axle stands and reviewed the setup.

Setup “A”

For the first time in pretty much ever I am going to put my cards on the table and show you my setup. If for any reason you decide to use these numbers, you can do so at your own risk.

I’m not racing anyone other than myself, so there is very little value in these numbers other than in comparison to other setups that I might choose to run on the car, or you might choose to run on your car, so enjoy!

VariableFrontRearUnitNotes
Camber-1.1 / -1.1-1.0 / -1.0degAt design ride height with setup pins in place
Spring Pre-load-3.0 / -6.04.0 / 4.0 mmAt the damper, full droop
Castor4.6n/adeg
Toe In-22mmDelta front to back across the axle over 300mm
Tyre Pressures1818psiCold
Spring Rate200120lbs/in
35.0321.02N/mm
Motion Ratio1.6701.128Wheel / Damper
Spring Rate @ Ground71.7194.3 lbs/in K/MR^2
12.5616.51 N/mm
Track Width14401390mm
Roll Stiffness227.30278.40Nm/deg0.5*K*w^2
* (pi/180)
% Roll Stiffness Forward44.95%
Weight245295kgExc. Driver, Full tank, Wet
% Weight Forward45.37%

So there you have it, all my numbers for the world to see. But which of these could be causing my instability issues? Well three of them stood out to me as potential causes for concern: the front castor, the front toe-in and the roll stiffness distribution.

Front Castor

So what does Castor do and why should we care? Here is a picture I stole from suspensionsecrets.co.uk. Some of their written text is a bit dodgy but their pictures are great!

That looks about right!

Increasing Front Castor:

Castor is the angle from vertical made by your upper and lower ball joints, as viewed from the side of the car. Increasing this angle moves the steered axis further forward of the centre of the tyre contact patch on the road, which is approximately where the lateral and longitudinal force is applied; this measurement is known as the “trail”. This causes the steering effort to increase for a given amount of load on the tyre, and the self centring moment to increase.

Why would that help my issue? Well I have straight-line stability problems and increasing the self centring moment means the whole upright assembly, and steering is less prone to wander in response to external steering inputs, like pot holes and bumps. It wants to go in a straight line.

From my experience working with small lightweight single seaters, albeit virtual ones, I know that 4.6deg front castor is very low for this weight of car. I remember Formula 4 cars running in the region of 7 to 10 degrees. In fact the weight on the front axle is very important when picking a castor angle, the lighter the car the more castor you have to run for a comfortable steering load.

The Downside:

I actually reduced the castor down to 4.6deg back in the summer of 2020, and for good reason. I have been running in the region of 7deg for a long time and was happy with the steering feel but I was really concerned about the additional negative and positive camber it induced at high steering angles.

If you look at the following pictures you can see the masses of inside wheel positive camber at medium to high steering angles. With the amount of camber gain that my suspension has its actually quite difficult to control camber, especially when the car pitch’s forward and backward.

But as you might have guessed, I have reluctantly put the castor back into the car as the steering lacks self centring and ultimately stability; its all a balancing act.

“How do you adjust the castor on your car?” I hear you ask? Well its really easy. The upper wishbone can slide backwards and is held in place by shims. This moves the upper balljoint backwards and increases the castor. It should be clear in the picture below:

Front Suspension with toe/camber plate and damper pins attached

Eventually I plan on changing the front suspension geometry to be a bit more of a compromise between pitch and roll, taking into account additional camber induced by castor.

Bonus Round: Bump Steer

Having increased the castor back up to 7deg I rechecked the bump steer and it was very very high; my notebook says +3mm toe out over 64mm of axle bump. I had to shim the outer tie-rods downward by about 10mm to remove any bump steer.

This was likely the source of a major handling issues I had back in the day while doing autosolo. In fact, the car was very unstable over bumps and would wiggle around when rolling into a corner; the following video kind of shows that.

I’m glad to have dialled this out. I have learnt an important lesson over the years: You can build a beautiful looking well engineered car but if it isn’t setup properly it’ll be dead slow.

Front Toe-In

With the virtual “Formula” cars they always tended to run some amount of front toe-out and rear toe-in. This made them very nimble and they would turn-in to corners easily. If you visualise it from above, it can be seen as the front inside wheel already turning into the corner.

Here is another picture stolen from the internet to help you:

Toe-in and Toe-out

In terms of stability I was always taught to visualise the car in a strong side wind. With toe-out when the car transfers weight onto the outside wheels it will want to turn away from the direction of the wind, this is unstable. With toe-in the car will want to turn into the wind, this is stable. Like a wind sock.

I decided to give toe-out a go back in the summer of 2020, mostly in response to the weird handling I had on turn-in, which was most likely due to excessive bump steer!

Given my stability problems, nimbleness was the last thing I needed, so I reverted back to a small amount of toe-in. I went from 2mm of toe-out, 1mm a wheel, over 300mm width, to 1mm of toe-in, 0.5mm a wheel. With the Ackerman steering geometry in the car this toe-in will quickly disappear with additional steering angle, but in a straight-line it just numbs the steering inputs.

“But how do you measure toe-in Josh?”, I’m glad you asked. With the car on axle stands, and pins in place of the dampers (putting the car in its “design condition”) I take the boots off of the steering rack and place 3d printed shims to lock the rack central; see the pictures below. I then attach “toe plates”, something of my own creation, onto the wheels and use a tape measure to measure across the axle. Adjustments to the wheel angle are made via the track rods. I also ensure the wheels are both running straight relative to the chassis and generally square everything up.

Steering rack with the boots pulled back (lock stops are in black)
White steering locks in place holding the rack central
You’ve seen this picture before- see the toe plate on the right hand side

The same method works for the rear.

Roll Stiffness Distribution

Roll Stiffness Distribution is something that is often ignored or poorly understood by weekend warriors such as myself but it is a core handling characteristic of a car, or should I say balance characteristic. In fact in F1 it was generally known as the “mechanical balance”, as opposed to “aero balance” or “weight distribution”. Its mechanically controlled.

My little Locost has no anti-roll bars so this is purely governed by spring stiffnesses and geometry; we’ll ignore roll centers for now, my front and rear roll centers are at approximately the same height.

Another stolen picture. I just liked this one and its semi in context.

I’m not going to dig deep into the whys and wherefores of how weight transfer works, that is not what this blog is about, but it would help if you agreed with the following things:

  • Increased roll stiffness on an axle, relative to the other, increases the given amount of weight transfer that axle experiences while cornering relative to the other. If the front axle is stiffer than rear axle, then more weight is transferred between the tyres of the front axle than the rear axle (sort of, this is a simplification, lets go with this for now).
  • Weight transfer on an axle reduces its potential peak grip and cornering stiffness, because this is how tyres react to vertical loads, and an axle is just two tyres. I’m not going to dig any deeper for this article.

All make sense? Great! If not, I strongly suggest reading a book like Tune to Win by Carrol Smith. There are loads of really readable references out there.

The final statement I am going to introduce covers an element of the system that I think is generally missed by most. It was somewhat of a “eureka!” moment for me when it was first introduced:

  • The further an axle is from the center of mass the greater the turning, or stabilising, moment it creates around the center of mass.

Basic physics right?

Given all of the above it would make sense that the further an axle is from the center of mass the less force it should produce, or grip, to keep the car in balance. This is the balancing of the front and rear turning moments.

Its not too big of a leap in logic to realise that if your weight distribution is towards the rear (say ~45% of the weight on the front axle) then your front roll stiffness should be higher than your rear and not ~45% of the total like my little Locost.

Some Basic Maths:

We’ll need to do some very basic maths to work out the roll stiffness of each axle and then adjust the front springs to change the distribution. Ignoring the contribution of roll centers and such, the roll stiffness of an axle can be calculated as follows:

I stole this from another website, and they ripped it out of a book, will we ever learn?

Well, that is kind of useless as we don’t have a solid axle with perfectly vertical springs attached to it, but we can turn the Locosts suspension into an equivalent axle by calculating the spring equivalent stiffness’s at the ground. We do this by using the motion ratio between the damper and the contact patch of the tyre. The maths is as follows:

I made this using math.tools/equation/image and paint

Where:

  • K is the stiffness of a spring, in Newtons per Meter, [N/m]
  • x is the displacement of a spring, in Meters, [m]
  • MR is the motion ratio between the wheel and damper, in Meters divided by Meters, its non-dimensional

Given the above equation we can calculate the spring equivalent stiffness’s at the ground and then use the track width (tyre center to tyre center) to calculate the overall roll stiffness for each axle. The distribution is then the front roll stiffness divided by the total roll stiffness (front plus rear, two springs in series).

The End Result:

I’ll reiterate the numbers from the table above:

VariableFrontRearUnitNotes
Spring Rate200120lbs/in
35.0321.02N/mm
Motion Ratio1.6701.128Wheel / Damper
Spring Rate @ Ground71.7194.3 lbs/in K/MR^2
12.5616.51 N/mm
Track Width14401390mm
Roll Stiffness227.30278.40Nm/deg0.5*K*w^2
* (pi/180)
% Roll Stiffness Forward44.95%

As explained, the front is softer in roll than the rear. How did I solve this? I increased the front spring rate from 200 lbs/in to 275 lbs/in, giving the following:

Variable Front Change Unit Notes
Spring Rate275+75lbs/in
48.16+13.13N/mm
Motion Ratio1.670Wheel / Damper
Spring Rate @ Ground98.61+26.9 lbs/in K/MR^2
17.27+4.71 N/mm
Track Width1440mm
Roll Stiffness312.55+85.25Nm/deg0.5*K*w^2
* (pi/180)
% Roll Stiffness Forward52.89%+7.52%

That is a whooping big change in Roll Stiffness Distribution, 7.52%! In the simulator I would usually aim for steps of 4% as these were usually noticeable, but I’m not messing about with the Locost. It was hideous to drive at speed and I wanted to feel confident in the car and enjoy it.

Setup “B”

The changes listed above amount to following setup differences:

VariableFrontChangeUnitNotes
Spring Pre-load-6.0 / -6.0mmAt the damper, full droop
Castor7.0+2.4deg
Toe In1+3mmDelta front to back across the axle over 300mm
Spring Rate275+75lbs/in
48.16+13.13N/mm
Motion Ratio1.670Wheel / Damper
Spring Rate @ Ground98.61+26.9 lbs/in K/MR^2
17.27+4.71 N/mm
Track Width1440mm
Roll Stiffness312.55+85.25Nm/deg0.5*K*w^2
* (pi/180)
% Roll Stiffness Forward52.89%+7.52%

The Result

After all of the above it was time for the fun bit: driving! So how does it feel?

  • The steering weight greatly increased. I can now feel the lateral acceleration build up and fall off with steering input. Its not uncomfortable but it is readable.
  • The car now tracks straight and doesn’t wander over bumps and dips in the road.
  • It still feels nimble and will quickly “take a set” in a corner; its not unpredictable.
  • Its not understeery or too stable, the balance of the car can be changed with the brake on entry and the throttle on exit.

But what does all of the above actually mean? It means the car is finally fun to drive! I went out for a good long session on a sunny sunday afternoon and people were waving me by and giving me the thumbs up. I managed to catch up with a group of Porsche owners out for a pleasant drive and give them a bit of a wake up with my bright red loud viper of a car. It was awesome.

Now I spend my days looking out the window waiting for the sun to shine… keys in hand… just waiting…

Locost: Airfield Testing

I get super nervous when it comes to things like this, logistics and towing always freaks me out. Getting the car to and from an airfield… on time… on a trailer… with all my tools and spares… there is plenty that can go wrong. Fortunately barely anything went wrong!

Setup

Prior to IVA I need a reasonable fuel map in the car so it can be driven around, undertake the emissions tested, test the speedo etc. I have changed so much in and around the engine that I needed to start from scratch this time around. Following lessons I had learnt running DIY fuel injection in my daily Sierra, I knew the benefits of using throttle position as the ECU load input, this is known as alpha-n tuning and is what I will be running in the Locost from now onwards as opposed to the blended tps/map setup I had been using before.

In short, I needed somewhere to drive and map the car. It had to be private land and with plenty of space to be able to drive at wide open throttle for long periods of time. After a visit to my local airfield, and a phone call with the very generous land owner, I was ready to go.

I made a big push to get the car into a ready state for the day, finishing with a pre-IVA job list of about six items. If all went well, I would be in a comfortable place to put in my paper work afterwards. Spoiler: my job list is now much bigger!

Journey

I barely slept the Sunday night before Mondays testing and after making sure everything was loaded correctly I arrived 15 minutes early at 9:45am.

Fortunately, my nerves amounted to nothing. The drive was a cool 1 hour 15 minutes with no hassles and very little traffic. Within half an hour of getting there my brothers Alex and Neil arrived to help me out, having driven for hours to get to the airfield. I love it when a plan comes together.

Initial Running

The first job of the day was to build confidence in the engine, shake down all of the many new components on the car and get some of the cruising fuel table positions filled in. Alex took to the drivers seat while I plugged in the laptop and watched the ECU do its thing and auto-tune the low speed elements of the table.

I did scoot the car around a little bit before everyone arrived and I could already tell it was driving better than it ever has, at least from a handling perspective. Over the winter I was very specific about the alignment I applied and made sure it was dead straight. The limited slip differential has also completely changed the feel of the car.

More RPM

After an hour or so of driving, and lots of stopping and checking for leaks, we started to build up the engine speed and mapping the wide open throttle (WOT) parts of the fuel table.

First 3000rpm, then 4000rpm, then 5000rpm and soon 6000rpm. The engine sounded loose and happy, free revving to whatever we threw at it. The auto-tune feature of Tuner Studio was pulling fuel out every thousand RPM we went up, suggesting my initial guess was too rich, exactly as I had planned.

Things weren’t entirely without incident and a number of issues became apparent at this point:

  • The front wing stays, on the rough surface of the World War 2 airfield, were far too soft. The wings themselves were bouncing around all over the place.
  • The clutch was progressively falling down the pedal. You could put this down to temperature but I was pretty sure the slave cylinder was leaking into its rubber boot. We removed the pedal stop to allow us to keep going.
  • The fuel filler tray gasket wasn’t doing its job and fuel was weeping out of the top of the tank. Eventually this went away as we burnt through fuel but would need to be fixed as soon as possible.
  • The fuel injectors were leaking at the manifold side, just a little, and the seals clearly weren’t sealing correctly.
  • Worst of all, the engine was burning oil badly on over-run. Sometimes clouds of it, sometimes not.

We decided to take note of the issues but simply crack on. Its not often you get access to an airfield for the day and we wanted to get the most out of it.

Calibrating the Speedo

I had a three point job list that I had to get done at the airfield:

  • Map the engine enough to get the car driving reasonably
  • Confirm the brake balance locked the front wheels before the rears
  • Calibrate the speedo

The first two were not a problem at all, but the third required a bit of thought. The speedo appeared to not be working at all, at least with the calibration I had put in at the beginning of the day. Based on my early maths, with a 4.3 ratio differential, and four bolts on the prop-shaft flange to read from, the gauge should have been seeing approximately 15000 pulses in a mile and that’s a what I set it to.

Given that this number was clearly wrong I adjusted the pulses per mile to 1000 and took the car out for a short drive, while referencing the GPS speed on my phone.

32 mph on the GPS, was 20mph on the gauge, at 1000 pulses per mile

My initial guess was super far off! How did I mess that up? Anyway, it was reading low, so by reducing the number of pulses per mile we could increase the speed seen on the gauge.

Doing a little bit of quick-maths suggested the actual calibration should have been 625 pulses per mile. Given that for the IVA the gauge has to read between the actual speed and 5% over we opted for 600 pulses per mile.

I did however want to back calculate my maths, which I will do here:

1 mile is 1609.34 meters
625 pulses per mile is 1609.34/625 = 2.574 meters per pulse

a 185/60 r13 ns2r tyre has a diameter of 552mm
this gives an circumference of 552*3.142/1000 = 1.734 meters

therefore 2.574 / 1.734 = 1.4844 full wheel turns per pulse

with a 4.3 differential ratio that is
4.3*1.4844 = 6.38292 propshaft turns per pulse...

that makes no sense

So yeah, the maths doesn’t add up and I don’t trust the gauge manufacturers instructions… but it works!

In fact, lets do some maths in the other direction…

4 pulses per propshaft rotation
4.3 propshaft turns per axle rotation
4*4.3 = 17.2 pulses per axle rotation

1.734m circumference gives 17.2/1.734 = 9.919 pulses/m

1 mile is 1609.34 meters
1609.34 * 9.919 = 15963.04346 pulses per mile

Now this kind of looks like the number we came up with in the end… can you see it?

15963.04346 * 4 / 100 = 638.5217384 ~= 638 somethings

Now the gauge manufacturers documentation describes this number as the “frequency”, so the factor of four kind of makes sense, maybe, and the factor of 100 could just be for the sake of storage or to give resolution for certain gearboxes.

Either way, done.

Driving on my own

Even though the engine was blowing a fair bit of smoke on up shifts we decided to get some miles on the piston rings and shake the car down further. Issues aside, it felt fantastic. Getting from a stand still to 70mph happens pretty damn quickly and the steering feel was better than it ever had been.

At the far end of the air strip was a number of coned gates setup for truck driving tests and I couldn’t help but have a little play in-between them. No complaints regarding the chassis.

Evolution of the Fuel Table

Below is the Volumetric Efficiency (VE) table we started the day with, the table we ended the day with and the difference table showing the changes made. The VE is simply a measure of how much fuel flow the ECU is demanding relative to the amount required to achieve stochiometric mixture at wide open throttle. Technically, if the engine is 100% efficient as an air pump, it would achieve 100% VE across the top of the table.

As you can see, the fuel table isn’t perfect, especially at high rpm and part throttle where it was barely touched. Its quite difficult to consistently drive this area of the table! I also did a substantial amount of manual adjustment based on what the wide open throttle numbers suggested. I could smooth it over more but I am going to leave it for now.

Notice that at low RPM the engine needs more fuel for lower throttle angles. This makes a lot of sense, as the throttle plates don’t act as much of a restriction at low flow rates, but as the flow increases at higher RPM’s they do a better job of restricting flow into the engine.

This map will do for the IVA, then I will take the little red car to the dyno.

Final Thoughts

I am really glad we got this day to shakedown the car. Its highlighted a few jobs that really need to be done before submitting my paperwork and its better to get them done now rather than later.

The engine is still a bit of a worry but my gut feeling is the valve guides have worn out. Prior to rebuilding the engine it had started doing the same thing and I had assumed it was the piston rings. The engine has fresh stem seals, so it points to the guides themselves. I have a spare cylinder head in great condition that I am going to drop in.

The chassis feels great and it was nice to have someone else drive it for a change. I’m looking forward to getting on the road later this year.

ManDoCar: Episode #3, Painting Dinghy’s, Man Do Compressor, Nissan Leaf Smugness

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”

Follow us on Twitter @ManDoCarPod

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] );

ManDoCar: Episode #1

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.

Dingy Chat

Pantone 333c Colour Chip

The Locost

New steering rack mount. Major surgery!
The chassis finally in a state to clean and paint. Spring 2020
Chassis all cleaned up and steering rack back in
Steering joint over the 10 degrees required for IVA
A very clean and red engine block
ARP Main Studs. Lovely.
Plastigauging a main cap
One of the old big end bearings. Not nice at all. These were new not long ago.
Inside of the drp sump pan.
New seat padding by JK Composites.
Bottom end back in the car.
The entirely wrong brake calliper slides …
… this is what they should look like
A freshly rebuilt and cleaned diff. Kaaz Limited Slip inside!
Auxiliary belt idler. Makes the engine much quieter.
Front lights! Looking great
Oil on plug #1. Not fouling, but not great. Need to do a proper break-in before any concern.
Hello!

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