Date: Thu, 13 Jul 2000
From: Mark Stonich MN USA
BTW I never use calculations to determine a recumbent's steering geometry anymore.
First, I determine the location of the rider's hands. For a street bike, I want the elbows 45-55 degrees from straight, and the knees coming up between the hands. (The orientation of the hands is just as important, but a bit hard to describe without illustrations, and irrelevant to determining the steering geometry. I have changed bars on other people's 'bents, such that the hands were in about the same location, but with a 15 degree change in orientation, and had them ask what I did to make their bike "more stable".
After the hands are located I draw an arc, centered on the center of the handgrip, with a 5-6" radius for an MWB or 6-9" radius for an LWB. Then I draw a line, tangent to that arc, to a point 1/4" ahead of the center of the front contact patch. That line is the steering axis. I determine head angle by measuring the angle between that line and the ground. The distance from the front axel, to the steering axis, is the rake (fork offset).
Date: Sat, 15 Jul 2000
From: Mark Stonich MN USA
Subject: Calculating trail
I always build my forks to give a small amount of trail when unladen, so that when the fork is under load, trail is near zero. On our tandem, rake is increased by about 5/16" when we get aboard.
BTW There are some situations where IMHO trail actually does help.
With a frame mounted fairing, sudden crosswinds will cause a bike with trail to steer momentarily away from the wind, setting up the bike to be leaned into the wind. Obviously lots of variables here, so predicting the proper amount of trail would be tough.
The right ergonomic setup will provide real centering force and more positive feedback than some combination of rake and trail. However, the ergonomics of most 'bents don't provide this, so many people have learned to use the negative feedback from wheelflop to help gauge what's happening.
If I ever get around to building the 2WD delta trike I have on the drawing board, I'll definitely want some trail to help judge side loadings, and to let me know when I'm losing traction at the front. Not sure how much, so I'll build an adjustable fork for a range of 1/2" to 1.5".
PS This will be my winter ride, so losing traction at the front is a "when" not an "if".
From: B beuershausenList-Id: Recumbent Human-Powered Trikes <trikes.ihpva.org>
Having raced cars for years, a bit of explanation of CASTER might help as it relates to handling. Caster is what makes the vehicle try to come back to "straight ahead" when it's moving. On my dragster, when you were going slowly and would try to turn, the steering was very heavy because you were actually "picking up" one wheel above the other because of the inclination of the king pin. That is what helps high speed handling and attempts to keep your car going straight down the road. Camber is the "leaning out or in" of the wheel at the top. Positive camber means the top is farther out than the bottom and negative caster is the opposite. Camber makes the tire "bite" when you are going around a corner, caster is what makes the vehicle "straighten up" after the corner and when you release the steering. Vehicles with not enough caster will "hunt" instead of track, and will not be stable. Toe-in and toe-out have to do with the tires are pointing inward or outward at the front. Toe in is needed so the vehicle will try to go down the road's center, while toe out has a tendency to pull the vehicle right or left based on the wheel that has the most pressure on it. Toe-out problems make the vehicle "darty" and unstable-quick on the steering, but not always in the direction you want to go. In a nutshell, the more CASTER, the more stability especially at higher speeds, camber is for planting the tire and making it "bite" in turns, and toe-in/out has to do with sensitivity to turning, toe-out making it very sensitive and twitchy.
From: Bill
Patterson wyms@lightspeed.netMailing-List: ListBot mailing list contact lowracer-help@listbot.com
Date: Thu, 16 Nov 2000
Subject: Re: [lowracer] Head tube angle
The simplified equations give pretty accurate results. However, they are just one part of the equation. The other is having too much trail and getting low speed fork flop.
My suggestion is to build a front fork with a long slot that allows moving the wheel BACKWARD from the fork. You can then move the wheel backward until it gives nice force feedback. At the same time you are increasing fork flop, which makes the bike hard to handle at low speed. A little flop is acts as an auto pilot and is good, too much jerks the handlebar out of your hand.
The force on the front wheel comes from the reluctance of the frame to experience angular acceleration. Without some Kx we don't get that.
I would love to get your bike out here and swing it to measure it's Kx.
I have been riding around on a tandem with 7 to 8 inches of trail with little problem.
The following program will give you some insight into the problem. It gives actual estimates for the
minimum trail to keep the bike from being too twitchy
and maximum trail to control flop. Hopefully, you will find good handling somewhere in between.
%% REM COPYRIGHT 2000 SANTA MARIA CALIFORNIA % REM FORWARD 10.00 $ PER COPY TO % REM 3058 LANCASTER, SANTA MARIA CA 93455 % REM THIS PROGRAM IS MEANT TO ACCOmPANY THE TEXT % REM "BEING THE CHRONICLES OF THE LORDS OF THE CHAINRING" %REM INPUT ALL ANGLES IN DEGREES pi=3.141592654; %REM we are metric deg = pi / 180; THIS INFO IS INPUT AS INCHES AND LBS and coverted to metric %REM A =wheelbase ; A = 63.75 * .0254
%REM B = dist from rear axle to cg ; B = 15.6 * .0254
%REM beta1 = head tube angle ; beta1 = 72
%REM H =distace from the gnd to cg "riders belly button" ; h = 10 / 40 %REM mass ; M = 123 kg %REM s= fork offset normal to headtube;
s = -1.5 * .0254 %REM Rh IS HANDLEBAR RADIUs Rh = 12 * .0254 %REM Rt is the tire carcass radius Rt = .5 * .0254
%REM KX = radius of gyration of the bike and rider about cg X axis %REM estimate .12 for supine rider to .6 for upright rider %REM more for a fully faired vehicle KX = .4
%REM beta = complement of beta1 BETA = (90 - beta1) * pi / 180
%REM r= radius of front wheel ; r = 6.75 * .0245
%REM CHANGE NO DATA PAST THIS POINT %' T = trail T = (r * sin(BETA) - s) / cos(BETA);
G = 9.81; ;
FLOP= (M*G*B/A)*T*CB/Rh %Maximum FLOP is estimated at 275, this may be high for some riders.
FLmax = 275; TMIN = 1.2*B/M*(1/(KX*KX)+1/(h*h)) TMAX = FLmax/((M*G*B/A)*CB/Rh ) TRAIL = T
--
From: Patrick FranzDate: Tue, 14 Nov 2000
Organization: TerraCycle, Inc.
Subject: [hpv] Re: Trail Troubles?
List-Id: Human Powered Vehicles Mailing List <hpv.ihpva.org>
. In a nutshell:
1. Trail and head angle aren't interchangeable, in that you can only partially compensate for one by changing the other. If you get either into unusual territory, the unusual one will dominate.
2. Trail and head angle are only part of what determines a bike's handling. Wheel diameter, tire width, tire inflation, wheelbase, mass distribution, frame stiffness, and handlebar location and width are all also important factors.
3. High speed and low speed handling can be very different. Hands on and hands off handling can be very different. Loaded and unloaded handling can be very different. A ride around a parking lot won't necessarily tell you much unless the handling is really awful.
4. A good quick test for neutral handling is a bumpy corner taken at medium speed (15mph/25kph or so). If the bike takes the corner confidently and without much bump feedback into the handlebars, the handling should be pretty good over a wide range of speeds and conditions. If you're afraid to take one of your hands off the handlebar in a bumpy corner, take it as a sign that the handling isn't dialed in.
A few hours of reading and rereading William Patterson's "Lords of the Chainring" class notes is a good way to bring a lot of the interactions into focus. If you're interested in bicycle handling, you've got to check it out.
From: Bill
Patterson wyms@lightspeed.netDelivered-To: mailing list lowracer@listbot.com
Date: Sun, 12 Nov 2000
Subject: Re: [lowracer] Head tube angle
Mike Nelson wrote:
Does anyone have any preferences on head tube angle for best handling on a lowracer ? How does head tube angle affect the need for trail ?
Head tube angle causes trail. It doesn't change the need for trail.
From my derivations trail needs to increase with B the distance of the center of gravity from the rear axle.
It also needs to increase as cg is reduced and it needs to be increased as the seat back reclines.
see instructions at the bottom of this site http://www.wisil.recumbents.com/wisil/trail.asp
The equations are in the wisil site.
The actual equation for trail is
Trail = [R cos( head tube angle) - S]/Sin (headtube angle)
R is front wheel radius S is fork offset sometimes referred to as fork rake I use the complement of the headtube angle so I may have the sine and cosine backwards.
As you lower the rear of your bike you are increasing headtube angle which increases trail just when you need it. Very synergistic