There was a thread over on F1 Technical earlier discussing the merits of a short versus a long wheelbase (incidentally one of many parameters I haven't nailed down). When I was thinking of how to reply it dawned on me that I had little objective or rigorous data to back up what my initial thoughts were. As a start, some might think that long wheelbase implies stability, whereas short wheelbase implies being nimble.
As a generality, I'm not really convinced that's true, at least thinking about it to a degree in 'derivative notation.' Milliken goes over this idea around page 149 of RCVD. In a nutshell it wraps some basic tire and basic vehicle concepts together into a fairly powerful but simple way of describing vehicle dynamics.
All other things being equal, a longer wheelbase should imply higher 'static' directional stability; if you split the axles apart further it should require more torque to 'dislodge' the car from a particular attitude. It should feel planted and secure.. but that's not to mean unresponsive. At the same time as you increase the distance from the front axle to the CG you bump up the control moment derivative; the front tires have a larger moment arm with which to act about the CG, and create higher yaw moment for a given steer angle.
Given that most of my regulars here have FSAE experience, the following example may be enlightening. If there's a series that needs sharp, fast, predictable response almost all the time.. FSAE is it. If you were to test the Goodyear D2692 and D2696 back to back on identical cars, you'd find some big differences in how they drive. The '96 generally should have higher response rates (cornering stiffness) overall, while in the same construction, size, etc. As such, the static directional stability is higher. The car can feel more settled and planted. At the same time it is much more precise and responsive to steering inputs, since the front response is also up! The '92 by comparison, with lower control and stability derivatives, can feel both vague and lazy. (The '96 also has higher ultimate grip, comes in faster, and has unbelievably good wear. Pretty good improvement.)
On the other hand, while the control moment derivative increases linearly with "a" (distance from CG to front axle), if you think of that front axle as a point mass it's contribution to vehicle yaw inertia increases with a^2. In theory then you'd think a car with a short wheelbase would offer higher yaw acceleration capacity. My question is - how much yaw acceleration do you fuckin need? "More" of anything is not always better, except for beer and scallops. I may have to see if I can dig up some old DAQ to see just how much you need. If you already have 2x the acceleration potential that you could realistically need.. why add more when there may be benefit elsewhere?
I'll let you marinate on that.
Tuesday, February 9, 2010
New mini project
This will be a good one, if / when I get it to work. One of my better ideas recently.. as usual, spurred by a couple beers. If you want a refreshing, mentally inspirational taste that's as cold as the Rockies, reach for a frost-brewed Coors Light.
Anyway, the idea is.. it will work like OptimumK in reverse... and consequently much more practical for the design engineer.
More to follow if I put something together.
Anyway, the idea is.. it will work like OptimumK in reverse... and consequently much more practical for the design engineer.
More to follow if I put something together.
Sunday, January 3, 2010
Into the New Year
Sittin here at DIA waiting for my flight back to Akron, Ohio... after an amazing time in Denver and Boulder.
Been busy at the end of the year, so it's been quiet around here. When I'm back, things will pick up.
Would be nice if design can get wrapped up in 2010. We shall see! Many things I'd still like to do.
In other news.. up to 47 followers now! Very cool.
Been busy at the end of the year, so it's been quiet around here. When I'm back, things will pick up.
Would be nice if design can get wrapped up in 2010. We shall see! Many things I'd still like to do.
In other news.. up to 47 followers now! Very cool.
Saturday, November 21, 2009
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.
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?
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.
Friday, November 20, 2009
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.
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.
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.
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