Round tube vs streamline tube

I'll preface this by saying I'm a big fan of "order of magnitude" approximations... i.e. spending an hour to get an answer that's 85-90% correct rather than spending a week to get an answer that's 95% correct. For any non-engineers out there.. there's really no such thing as an exact answer in a lot of this stuff. Just a question of how accurate you want to get. In my opinion some people get too caught up too early with trying to find an exact solution.

This goes along with my long-standing belief that 'perfect' is the enemy of 'good.'

It's useful to do this stuff to get an idea of where you need to focus your work. And while yes, every little bit of performance you can squeeze out of a racecar is important, you also have to keep scale in mind. Let's say for example I know I can get an order of magnitude improvement in drag... is that 100 lbf versus 10 lbf? 10 lbf to 1 lbf? Or 1 lbf to 1.6 oz? When you can easily sidetrack yourself working on a million things at once, you've got to go after the low hanging fruit first, and really ask yourself, "What is the most efficient use of my time?"

Anyway, onward. Since aerodynamics aren't my strong point, you're all welcome to check my math.

When fabricating control arms and pushrods you've basically got two choices for tube profile. Round (as I've shown so far in CAD for simplicity's sake) and streamline. This particular streamline tube profile is available at Chassis Shop (they have some damn good pricing on CrMo tube!). While it's cool looking and tempting to use on everything there are also some definite constraints. It's generally 3-4x more expensive than round tube, it's more difficult to fit to itself for welding, and you have to make special end adapters for your rod-end and spherical bearings. This particular one I found on the Baumgartner Race Car page.

In order to justify the added expense, we should have a pretty damn good reason for using it.

Aerodynamic drag is generally given by the following equation:
Where F_d is the drag force, rho is fluid density, v is relative air speed, A is exposed frontal area, and C_d is the dimensionless drag coefficient. You had damn well better get your units straight for this one. Using Imperial units, density should be in slugs per unit volume.

C_d itself varies significantly with shape and with Reynolds number. For this particular analysis I'm assuming relatively high Reynolds number flow, where the drag on an infinitely long cylinder is around 0.5, and drag on a streamlined object is around 0.05.

I'm making a gross simplification and calling each control arm and pushrod a single tube exposed to the oncoming air. I'm also going to say they're all 0.625" diameter tubing, and all roughly 18" long. That gives me a grand total of 135 sq. in. frontal area. For velocity we'll use 100 mph (1760 in/s). For density we'll use 1.2 kg per cubic meter, which works out to 1.347e-6 slugs per cubic inch.

Turn the crank and I come up with 140.8 lbf drag. Given that it takes about 0.00267 horsepower to push 1 lbf at 1 mph (power = force * velocity)... at 100 mph that comes to 37.6 hp. That's quite a bit for a ~180 hp engine!

If I use streamline tube of the same height, since C_d goes down by a factor of 10, so does drag and power. 14.1 lbf drag, and 3.8 hp. Or in other words, going to streamline tube frees up 30+ hp at high speed. Looks like I'll be taking that approach. Realistically that might not mean an awful lot in terms of increasing drag-limited top speed since the tires and chassis have massive frontal area, but a couple extra mph makes a difference on a long straight.

Just for some perspective, if you were to do the same thing on a FSAE car... let's say at the top end of an acceleration run you're at around 60 mph. Let's assume we're using the same tube shapes and lengths. That's a reduction from 50.7 lbf to 5.1 lbf, and 8.1 hp to 0.8 hp. On a FSAE car then you'd expect to "free up" an extra 7 hp at high speed. On a restricted engine that's only making probably 75-80 hp to begin with, that's a non-trivial amount. To prove it to design judges of course you'd probably want to find a long stretch of asphalt and do acceleration, top speed and coast down runs with both styles of control arm. That'd be an interesting experiment and a good junior project.

Steering and alignment settings (part 1 of ?)

Getting late and this may get involved... but we'll put on some Wes Montgomery and start at taking a crack at it. Steering (Ackermann) and alignment (toe) settings are an important design and tuning point, but for us at least seemed to be last on the list of things to adjust. More often than not I think we never really did much of it!

Even if you wanted to tune it on the skidpad or a simple 'squared off' course you've got plenty of combinations to run through if you take the brute force approach:

• Front axle: Toe in? Parallel? Toe out?
• Rear axle: Toe in? Parallel? Toe out?
• 'Static' Ackermann: Generally positive? Parallel? negative?
• Ackermann 'progression': No change? Transition toward more negative at high steer angle? Transition to more positive at high steer angle?

Bearing in mind that in theory, those above parameters can change based on changing static camber settings or bolting on a different set of tires, or even just by adding or removing roll stiffness (changing dynamic camber).

That's a bitch. Good luck track testing all of that and getting any sort of consistent read on subtle changes.. when the track is evolving (rubbering in, changing temp).. while ambient air temp is changing (slightly changing downforce, drag, and engine power).. and as you're wearing down tire sets. Really I think the only good way to do it is by using tire data, which hopefully (but not always) is sufficiently accurate.

Even then, you have to know what you're designing for. In my opinion a good part of it is getting the left and right slip angles "matched" so the tires saturate at the same time. Wish I had a good graphic to describe this. Maybe tomorrow. But let's say at a given limit cornering loading your outside tire peaks at 6° slip angle and your inside tire peaks at 8° slip angle. The left and right wheels really aren't that independent, so the only way you're going to get the tires to both peak at the same time is to run some pro-Ackermann steering and/or toe out. Otherwise if you had been completely parallel and steering both tires to 7° you'd be overdriving and abusing the outside tire while underutilizing the inside tire. I'm not sure of a great way to determine this using telemetry without using wheel force transducers.

That's my limit steering strategy. On-center (near 0°) is a bit more difficult for me to grasp. Intuitively I'd think you wouldn't want to run dramatic amounts of toe in any event as it will slow you down on the straights (tire is generating lateral force but starting to point backwards).

The thing that I'm not convinced of are the "conventional wisdom" that toe-out on the front "helps turn-in," toe-in on the rear "helps rear stability," and that any amount of toe-out rear is going to make the car a bitch to drive. The reasons why are not obvious to me at the moment. I'll have to think about that. With the rear tires anyway, if they don't peak at the same point (and chances are with your luck they won't) you're invariably leaving grip on the table unless you can split the slip angles a bit!

Long story short: "Limit" steer settings are a hell of a lot more obvious to me than on-center ones.

The Following

24 people 'officially' follow this blog. That is cool! I recognize a couple FSAE names outside of CU. Even cooler. Hope this is at least interesting to read.

If you do check up on this regularly, don't be shy. Click that follow thing over on the right. I think so long as you've got a Google / Gmail account (why the hell don't you??) you don't have to sign up for anything. Lets me know people are enjoying it.

Cool feature on the Ferrari F60 brake system

Little did I know Rob Smedley speaks pretty decent Italian. Better than mine. Then again when you're 'Phil' Massa's race engineer at Scuderia Ferrari I suppose it makes sense. Some Italian reporter caught up with him and asked some questions about the '09 car.



For those of you who understand even less Italian than I do, here's what I interpret as roughly what he's saying:

For a while he's going on about the seat, how they mold each one to each driver, et cetera. Then he gets into the steering wheel and describes some functions, but those are generally well-known. At 2:40 he gets to the cool part about in-cockpit brake adjustment.

The lever and the knob both make brake balance changes. The settings are something to the effect of baseline, and +/- 1% front balance. So for example if you have a really high speed braking zone with heaps of downforce and forward load transfer, you'd flick the lever forward to add some front balance. A couple corners later if you've got a low speed braking zone without as much load transfer, you can flick the lever back to get a little more bite on the rears. The nice aspect is you can quickly, easily, and repeatedly get to the same bias settings without having to constantly screw around with a knob. I'd suspect as little as 0.5-1% balance change is noticeable.. so being able to make repeatably adjustments is key.

The knob acts like you'd be used to in a racecar and makes a 'global' balance change, for example as fuel burns off or as the front or rear tires go away. So, let's say your lever positions are 54%, 53%, 52% to begin with, a twist of the knob might make them 55%, 54%, 53%... and another twist 56%, 55%, 54%.

How applicable is this in a F1000 chassis? Good question. May have to think about that, though initially I'd suspect it's probably not worth it. The top speeds and downforce are just not going to be the same. Doubt many F1000 drivers are braking at 5G.

Cool feature though.

Another note on force-based centers

Got to thinking about this some more, and how you'd determine your centers in advance of K&C testing. Really just comes down to a somewhat involved statics problem. If I remember right, Racecar Engineering had an article at some point in the last year that showed how to go about solving it, but they did leave out one big item in their simplification. I'd actually suspect it's one of the bigger points for why the true centers digress from the kinematic centers.

I've kind of gone over this point before, but I've made more sense of it to myself now.

Under high lateral load, the tire - being the non-rigid structure that it is - deflects in a couple different directions and moves laterally under the wheel. If you have your own racecar and put a camera watching the tire footprints you can see it pretty clearly, even on a FSAE car.

This gives rise to a non-zero overturning moment at the contact patch (not to be confused with the total overturning moment at the hub, which also comes from lateral force and puts substantial radial load into wheel bearings). Alternatively you could think of this as the vertical reaction force vector moving laterally with the tire. I believe in the RCE article they just assumed a purely lateral and vertical force, at a fixed position.

In any event, you'd think that adding that moment would change how the forces are resolved through the suspension links, and thus how those lines of action act about the CG. The greater the deflection of the tire, the greater this effect. While I had realized that tire Mx played into total load transfer, I didn't know how it was distributed.. be it as a geometric or elastic effect. I'd think it would be purely geometric, at this point in my understanding.

As an interesting consequence, bolting on two different tire sets, even of the same size, could result in different true roll centers (force application points, whatever you'd like to call them) when out on the track.

Really, Bridgestone?

In an online article in Racecar Engineering, they made a note of the new "slim" front tires Bridgestone will be running in their final year in Formula 1.

Interestingly enough, they included a drawing of the inflated profile of the provisional 2010 tire compared to the 2009 front, including a labeled scale!

Big differences between the two profiles. That will be a substantially different tire. Also hadn't realized that they were using 12.75" wide rims. While I understand the teams would be very interested in getting that for doing aero simulation, I'm surprised they made it totally public. Then again I'm sure no one at a rival tire company would digitize it and put it in CAD or anything.

Side project to the side project

Ohh y'know.. just a cool toy to have around and play with (a 1990 Penske Indy Car)



All in a (couple) day's work. Went together very smoothly with help from the lead engineer at the Vintage Metal Works.

Not the best design, if you ask me. Few interesting points. All the dampers are a pain in the ass to get in and out, given that they're all vertically oriented, rather than horizontally (which has become the more popular trend these days). You can adjust the front dampers from the cockpit however, along with front and rear bars, and brake bias.

A total of 4 (!) bolts hold the monocoque to the engine. That's it. Not very large ones either, all less than 1/2" diameter if I remember right.

Also, for those curious... yes, it is this yellow car... which finished 4th at this particular race.



I really like the eye-level onboards better than the roll bar stuff. Much better feel for what the driver is seeing and doing. Feel free to watch the commercials from 1990 at the end, haha.

Torque and power

Not even sure how I got to this thought, but I can't sleep anyway.

The "which is more important.. torque or power" debate is popular in shop talk, and if you ask me, pretty dumb. I believe there's even the saying, maybe even from Carroll Smith himself, "horsepower sells cars, torque wins races" or something to that effect. The two are so closely related with speed it makes absolutely no sense to compare the two as separate entities. Let's go over some simple concepts though.

With a large enough gearing, I could turn a crank with my feet and make more output torque than a Formula 1 engine. That doesn't do me any good however, as I'd never be able to turn the crank at that load, at a high enough speed to make anything of it.

To accelerate an object (read: car) to a given speed requires an energy input. Pure and simple. To get a car up to 100 mph requires a fixed quantity of energy transfer, I don't care how you do it. You want to get this done in the shortest time possible. Work over time is power. The quicker you want to get to 100 mph, the more power you need.

There is however also an acceleration requirement to get to a given speed in a given amount of time. That requires a fixed value of average thrust at the tires, and thus torque. If I had a really high power engine with extremely long gears, it would do me no good as I'd never produce the required thrust to do anything useful.

To achieve maximum acceleration, there is an engine power and WHEEL torque requirement, and the two are related by gearing. That's all there is to it. Keep in mind of course, if you have a high power motor and you're not developing enough thrust, you can always gear it down to bump the torque up. You can't however pull power out of your ass.

Another way to think of it is as such. To keep a car going 100mph you have to overcome some amount of drag. Drag force itself lends itself to a torque requirement... but force times velocity is a power requirement.

Or, think of what the race engine is basically required to do. You want to burn the most fuel as quickly as possible, and efficiently as possible (without blowing up). You want to be able to release as much as that chemical energy in the fuel as possible in the shortest amount of time (again, maximizing how much mechanical power is made). To that point, to burn more fuel, you generally need more air. As a corollary, for a given mass flow rate of air there's only so much fuel you can burn, and so much power you can extract. For you FSAE folks, as a fun challenge, find the maximum mass flow rate of air you could possibly hope for, through a 20mm restriction. Find how much power can generally be extracted per unit mass flow of air, and then find out the most power you could hope to get out of it.

It's fun comparing the maximum theoretical power output of one of those restricted motors with how much some teams claim to make, ie the guys who say they can make more. It is good to know though, what max RPM your engine should be choking the restriction at. I really wish we'd had the time to get some cams made up designed around that. Oh well.

In any event, going by peak values, as is typical, is as meaningless in my opinion as calling a car "tight" or "loose." Really doesn't tell you anything. Area under the curve seems like it would be the more important parameter.

Edit - Was originally gonna include some thoughts on the claims of some engines to "give tires time to rest between cylinder pulses and regain grip" but I'm saving that for another day.

Rear damper packaging

I'm thinkin'... somethin like this:
Though I will probably move the rear chassis-side point of the upper a-arm rearward. This should allow me to use a damper with more travel (3" in place of 2"), and will also look cooler!

Still need to come up with a good way to mount it to the frame...

And where I'll put the R-ARB..

Regarding Titanium...

Holy shit. I take back what I said.

Initially, to do the crazy (and probably dumb) idea of making those tripod housings out of billet 6-4 Ti, would have been about $467 / part in raw material cost. Found another place that can supply it for $182 / part. $182 for a 3" diameter x 3" long bar of certified Grade 5 Ti. That's pretty reasonable, even though 416 or 4130 would be ~$30 / part.

Handful of Ti parts on the car would pull 10 pounds out. May be worth keeping in mind.

More drivetrain solutions

Have to give credit here, had the idea from something I saw on an old Western Washington FSAE car.

Instead of transmitting torque by a bunch of small involute or straight spines, they apparently used a large "sinusoidal spline." At least with this approach it's easy to CNC mill the external and internal pattern (CNC milling cost is a non-issue). Lets me ditch the dowel pin pattern approach. On these parts I just have a placeholder shape, until I can figure out how best to draw this damn thing.

Redesigned some stuff, starting with the tripod housing, which now also incorporates the features that drive the hub (had been 2 pieces previously). Total weight of this unit, made from steel, is about 1 lb, which in itself is roughly a 1 lb reduction (!!) from the previous arrangement. If I made this piece from billet Titanium, I could shave off even more. I think we can all agree that would be baller extreme. However, the stock material cost for enough 3" diameter Titanium bar to make two of these is roughly $1,000, whereas I could have enough stock for three of the things in 416 stainless for less than $100.

Additionally the hub can now accept this pattern.

The two mate together as such.

In this way, the drive shaft is held to the hub and upright by means of a single nut, which is accessible even with the wheel still on the car (by putting a socket and extension down the center bore of the hub.


Might even work.

Drivetrain solutions

A couple ideas anyway.

First up is the driveshaft itself. The general Taylor Race arrangement is as follows...

Splined halfshaft into a tripod CV joint. That joint sits in a roughly inch thick housing, open on both ends. Torque is then transferred from the halfshaft, into the tripod by a spline, into the housing by direct contact, and then into the hub flange by the 6-bolt pattern. I don't like having 6 wired fasteners to take apart, and I don't like the open end on the tripod housing. As soon as you take it off, grease goes everywehre and you have to make sure other crap doesn't get in there.

I like the idea of sealing off one end of the housing, as shown above. It becomes a bit thicker, but by going to aluminum the total weight is considerably down. While bare aluminum likely wouldn't hold up to the Hertzian stress imposed by the tripod rollers... a thick, hard anodize or hardened steel sleeves might be up to the task.

Still haven't figured out a good solution to using less fasteners, and getting rid of safety wire while still having an easy positive stop on. I'll have to think about that.

I'll add, I'd like to avoid cutting splines where possible. Expensive, and not always necessary.



I am thinking about something similar to the above for a diff housing carrier. I'd like to have an assembled, billet "diff box" that holds the suspension and differential. Placement of everything will require some creative packaging. This way however, the diff can pivot and rock back and forth on the bottom mount, allowing chain tension adjustment. By undoing the two long bolts, the whole diff can be rotated 90 degrees and then slid out from the left side. That large opening in the plates is longer than it is tall.

Drivetrain challenges

Jumping around a bit here from suspension to drivetrain, but I don't want to get too locked into the component level (actual control arm geometry) until I do some more parametric design (getting a good read on what camber curves, etc I want).

On our FSAE cars, while the drivetrain layouts we used were generally functional, serviceability was lacking. I wish I had some pictures to illustrate, but for now it appears the remote CU Durning Lab login is down. Anyway, items requiring service:

1. Adjusting chain tension. Invariably we had to do this as chains wore in, when going with a different sprocket arrangement, or when replacing a chain. We generally used a two turnbuckle arrangement holding the diff carrier to the frame, so alignment and position could be adjusted. It wasn't ideal, and certainly wasn't fast.
2. Replacing driveshafts. While we never broke a shaft, these had to come on and off for a variety of reasons. Snapping a shaft definitely is a possibility with a higher power car. In any event, our setup was a splined shaft, with a tripod and housing on both ends. Total of 12 socket head cap screws (SHCS), in 6 pairs of safety wire, had to come out to get the thing off.
   
   Not to mention, the process was a mess and you'd wind up putting bags around everything to keep from losing all the grease and what have you.
   
3. Swapping sprockets. You'd have to take tension off the chain, undo another 6, safety-wired fasteners, and get the thing off. Time consuming.
4. Removing the diff. Similar story, time consuming. Remove tensioners, cut safety wire, undo 12 bolts, take it out, do whatever, replace it, 12 bolts in, safety wire them all.

Time to think up some solutions that make all those quick and easy. Maybe I'll have some CAD this afternoon between games. Giants @ Eagles, Vikings @ Packers, Yankees @ Phillies.

I'd be happy if both teams from Philly lose, and if it's a good matchup at Lambeau.