# Handling Qualities for Bikes and Recumbents

• Ran D St. Clair's series on handling

• From: Carey Chen
In particular to lowracers, especially SWB, conventional head angles (70 to 72 degrees) with a trail of 50mm (2") is about all there is. This I've found to be the case for my designs because of how the frame has to be built over the front wheel. Too slack a head angle and the heel overlap increases, too steep and the rear part of the front wheel comes very close to the frame and one's crotch. I generally use a head angle of 70 degrees, and a trail of 2" to 2.5". All the lowracers I've built use a 20" (406) front wheel. A 16" (349 or 305) front wheel would allow for more variations in the head angle. Unless you have an inseam of 33" or more there would also be room for variation with a 20" front wheel.

• From: Bill Patterson
CONTROL SENSITIVITY
High speed bikes need to have a reasonable "control spring" so that the controls will be harder to turn as the speed increases and control authority gets higher. Its similar to turning down the sensitivity of a computer mouse.
We have used our values for the control spring and maximum sensitivity to arrive at minimum values for trail that will make high speed bikes easier to control.
T = 2.5 (B/m)(1/(h*h) + 1/(kx*kx) )
This equation neglects the front wheel angular momentum. Bikes with 27/26 inch front wheels should use
T = 2.0 (B/m)(1/(h*h) + 1/(kx*kx) )
All measurements are in units of kg and meters.
(A ) Wheelbase
( B ) the horizontal distance from the rear wheel contact point to the cg
( h ) the vertical distance from the rear wheel contact point to the cg
( m ) Mass of the bike and rider
( Kx) Longitudinal radius of gyration through the cg.
(T) Trail

As the radius of the front wheel is reduced, trail must be increased to compensate for the reduction in the angular momentum of the front wheel. This is just the opposite from the original idea of designing to a castor angle. In fact, most questions about the lack of feel from smaller wheels is answered as an angular momentum problem. This is false.
The reduction of trail is the primary culprit.
The concept that the position of the seat and the orientation of the seat back are the prime factors in determining trail is somewhat surprising. This concept was highlighted when I recently started riding a low racer with an adjustable seat. When the seat is tilted back to 50 degrees from the horizontal, the 3 inches of trail is barely adequate. I then tilted the seat to 25 degrees from the horizontal and the bike became a "wet noodle". I certainly didn't have proper control feedback.
Most bikes have the factor of 1/(h*h) to be 2 or 3. For a low racer is can be8. The seat back can have a much greater effect. The factor 1/(kx*kx) will be 10 for a 50 degree seat back, but it goes to 25 as the seat back is reclined to 25 degrees.

We are only making educated guesses as the value of the Radius of gyration. The presumption is that the rider overwhelms the geometry of the bike, so we concentrate on the rider. The following are guesses and measurements, but are to suspect.

A vertical man/rider Kx = .6 meters
A diamond frame rider Kx = .4 meters
A vertical seat recumbent Kx = .35 meters 90 degrees
A reclined seat recumbent Kx = .3 ,meters 50 degrees
A laid back seat recumbent Kx = .2 meters 20 degrees

We have been working this problem for some time and will have better numbers in the future. These are for the X axis they are not through a principal axis.
Bill Patterson
Assoc. Prof. Mechanical Eng. CALPOLY SLO
"Lords of the Chainring" Handling qualities theories for bicycles and motorcycles (90+ spiral-bound pages)

• The effect of frame geometry on handling qualities - see Issue52.pdf in the BHPC Newsletters section.

• From: Warren Beauchamp
.... Here's the way I think the trail works, please correct me if I'm wrong:
Draw a line through the center of the head tube to the ground. If the point the line intersects the ground is before the tire, that means you have positive trail. If that point is behind the tire, that means you have negative trail. Varying the amount of rake on the fork adjusts the tire to intersection point distance forward and back.
I have been designing my bikes with around 2" of positive trail, which has worked well for me in the past, but Felix's design seems to be for 3" of negative trail. These two conditions should be worlds apart in handling.

• From: Don Ferris - Anvil Bikeworks
The rake and trail spreadsheet is now on my website as is the always frame variables/geometry.

• Qn:- Does anyone have a recommendation about how much trail a delta trike's front wheel should have for good handling?

A:- I would recommend 1/2" to 3/4".  Less if you have little or no tiller in the steering.
One thing you have to do when converting a motorcycle for sidecar use is to reduce trail to about 1/3 to 1/2 of the trail it had when it was a leaner. I have ridden motorcycles with sidecars where this hadn't been done, and the result was horrid.  So much effort was needed on the (wide) bars that you could actually see the forks twist.
Trail doesn't make the front wheel go straight anyway.  It allows the wheel to be steered by sideloads.  On a wedgie this allows the bike to be steered while riding "no hands" by applying side forces to the pedals.   (This has been known for over a century, it's spelled out in Sharp's book). Hard to do on a recumbent, but SWBs with large amounts of trail suffer from pedal steer.
BTW I am careful about steering ergonomics of my 2 wheel recumbents, so most people who have ridden them think they handle great.   Yet none of them have more than 1/2" of trail, some have almost none.
Mark E. Stonich   Minneapolis, Minnesota Human Powered Vehicle Assn.

• Trikes, like bikes and motorcycles, generally benefit from using a slanted head tube (steering axis) as it makes it easier to have the tire contact patch BEHIND the intersection of the steering axis with the ground (by a distance called trail, positive trail).  Then, when the front wheel is turned, a reactive force at right angle to the wheel is produced and acts on a lever arm (approximating the trail) producing a correcting torque which helps straighten the wheel and so provides directional stability.
In contrast, when the contact patch coincides with or is in FRONT of the steering axis (negative trail), the torque generated doesn't help straighten the wheel and may cause instability. Not good, as you have already found out.

The classic formula is trail =  R / tan P - Q / sin P where R = radius, P = angle of head tube relative to the ground and Q = fork offset
Most of the road, track, and touring frames I have built have had trails of from 55mm to 65mm. Whether this is also the optimum range of trail for 20" and smaller wheels is really unknown (to me). I don't believe the front wheel drive aspect is relevant except that the linking of the wheels and the frictions in the drive and steering linkages may damp out (overwhelm?)  the self steering effects that trail may provide.
There was a fairly extensive discussion of this topic on the hardcore bicycle science mailing list a few months ago. You might find it on dejanews.
You might "design by consensus" or better yet build a trike where the head tube angle and the fork offset can be adjusted and experimented with.
Hugh Enox

• From Colin Lewis
I built a FWD delta trike, and I can tell you my experiences.
To keep things simple, I have a vertical (90 degree) head tube and a backward-facing BMX fork. By itself it gave about 1" of trail. The cranks are in front of the fork, and the chain is routed by two pulleys from the frame, down the back of the fork and back up the front of the right side of the fork.
The result is that the trike is very easy to steer, but it goes into violent oscillations if you take your hands off the bars! This happens even at slow (3 mph) speeds.
I tried bending the forks back another inch but it does not make any noticable difference.
I thought I had a flexy frame, but it is 2" x 2" .065" wall square tube. It doesn't seem to be flexing. I decided that what is happening is this:
The steering gets a slight deflection to to one side, say the right ( as if you were making a right turn.)
This puts the contact patch to the left of center, because of the reversed fork.
Contact patch forces push the contact patch back to center, rotating the steering to the left. Since we are rotating around the contact patch, the mass of the trike is forced to the left.
When the contact point reaches center, the momentum of the mass of the trike moving right to left causes it to continue, which displaces the contact patch to the right.
So the trike ends up oscillating around a vertical axis.
I haven't figured out yet what effect a slanted head tube would have.
• Date: Wed, 28 Jun 2000 13:31:45 -0700
From: Bill Patterson
To: Lowracer
Subject: Re: Fork Problems
Guzman wrote: Are there any handling downsides to steep headtubes? Shallow?
We have tried many of these solutions. Trail by itself aids control by increasing the control spring. ie how much added force is needed to move the controls. Some people like more force, some people like less force.
This control spring also can be changed by tiller (hands aft of the steering axis) or stem (hands forward of the tiller). If you use tiller, make sure that your hands are far from the body so that you generally pull on the handlebars.
A more vertical head tube is preferred because of low speed negative control spring effects. you can feel the handlebar tend to continue into the turn. This effect causes control problems at very low speed. This is reduced by using a more vertical head tube. Check out the front end geometry of the new Bike2 tandem.
Building a "boiler plate" variable geometry bike is an education. We find that a vertical bent back fork gives good handling throughout the velocity envelope of a bike. Of course, if you plan on spending very little time at low speed, a vertical fork is of no value.
The wisil web site has a simple equation out of the Lords of the Chainring, that will allow you to estimate minimum trail for your proposed geometry. The value 1.5 is low in my opinion, but will give a bike that is controllable. It will feel like a criterium bike. Sometimes we can't use the best trail for highspeed bikes because it introduces other control problems. That's why I tried to use the absolute minimum value of trail for the wisil lowracers. 2.5 is better for us mortals.
Ain't bikes fun???

• Date: Tue, 27 Jun 2000
From: John Funk
To: Lowracer
Subject: Re: Fork Problems- Working out rake angle

You may not believe me but this is how it was explained to me and it works perfectly.
1. Draw a line on a piece of paper. This is the road .
2. Draw your wheel on top.
3. Pick a point about 1.5" infront of the contact point, this will be center of pivot.
4. Figure out where you want your hands.
5. Put a mark between 4 and 8" in front of your hands. This is the tiller. 4" will feel quick to the point of being squirrely 8" will feelheavy and a lot more stable. If you decide on less than 4" many people will feel unsafe on it, I know because i have one.
6. Draw a line from the spot from #5 to the center of pivot from #3. This is the line you should place your head tube on.
7. Measure from the head tube line to the center of the wheel and you will have the rake needed for your fork.

I didn't believe this when I first had it explained to me, but recently I broke the handle bar on my SWB. when I repaired it I wound up with more tiller in than I had before, and the bike went from being difficult to ride to almost normal. I went from 0" of tiller to 1" of tiller and it made a huge difference. Before to get the bike rideable I had about 4" of trail with the forks almost straight. I really should put more tiller into the handle bar to get it closer to 2.5"
That is the little bit that I know about front ends, thankfully it works whenever I need to design anything, so I don't really work on design past using this method.

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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).

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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 beuershausen
List-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.net
Mailing-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 Franz
Date: 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.net
Delivered-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