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"
From: Bill Patterson
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
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.
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
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.
Longitudinal Radius of Gyration
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.
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.
.... 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
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
From: Don Ferris - Anvil
The rake and trail
spreadsheet is now on my website as is the always
- Qn:- Does anyone have a recommendation about how much
trail a delta trike's front wheel should have for good
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
- 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
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
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.
- From Colin Lewis
I built a FWD delta trike, and I can tell you my
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
- Date: Wed, 28 Jun 2000 13:31:45 -0700
From: Bill Patterson
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
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
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.
- Draw a line on a piece of paper. This is the road .
- Draw your wheel on top.
- Pick a point about 1.5" infront of the contact
point, this will be center of pivot.
- Figure out where you want your hands.
- 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
- 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.
- 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.
- Mailing-List: ListBot mailing list contact email@example.com
Date: Thu, 13 Jul 2000
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).
- Mailing-List: ListBot mailing list contact firstname.lastname@example.org
Date: Sat, 15 Jul 2000
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
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
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
Mailing-List: ListBot mailing list contact email@example.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
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
h = 10 / 40 %REM mass ;
M = 123 kg %REM s= fork offset normal to
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
%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;
%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
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
Delivered-To: mailing list firstname.lastname@example.org
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
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
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
As you lower the rear of your bike you are increasing
headtube angle which increases trail just when you need
it. Very synergistic
Thursday, 29 January 2009