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article 17, issue 05


Ergonomics of Direct-Drive Recumbent Bicycles

Jeremy M. Garnet
December 21, 2008

Abstract

The direct-drive recumbent bicycle has the crank axle concentric with the front wheel, and a planetary gear front hub. This design offers the advantage of simplicity, good weight distribution and a large load capacity—but has the disadvantage of pedal force feedback to the handlebars due to the fork mounting of the pedals, and excessive front assembly mass due to the weight of the rider's feet on the fork-mounted pedals. This paper explores force feedback as a function of head angle and a method of calculating an additional centering spring is presented. A variable-geometry bike is used to give a qualitative, real-life assessment of the results, and to explore the human-factor issues unseen in the equations. Finally, a suitable design configuration is presented.

[Editors' note: this is a condensed version of the article without any equations and only some of the diagrams. The complete article may be downloaded as PDF (600 kB) by clicking here. The figure numbering differs between condensed and full versions.]


INTRODUCTION

The direct drive recumbent bike

The direct-drive recumbent bicycle has the crank axle mounted on the front fork, concentric with the front wheel axis. Gearing is provided by a transmission in the front hub. Figure 1 illustrates the basic layout of the author's direct drive recumbent.

Figure 1
Figure 1: A direct-drive recumbent bicycle

This configuration results in a very simple bicycle with no chain, and it allows a full-size front wheel to be positioned for ideal mass distribution and braking stability. The result is improved low speed balancing, a smoother ride, lower rolling resistance, and more effective braking. In addition, this can all be achieved with a user-friendly seat height and low bottom bracket, making the design well suited for in-town riding. The cargo carrying capacity of the direct drive recumbent is impressive due to the amount of space made available under the seat. 

A brief history

The earliest bikes had directly driven front wheel drive. The ordinary, or high-wheeler is an example. As early as 1892, a planetary gear hub and a smaller wheel were available to replace the huge front wheel—but this design was largely overshadowed by the enormous popularity of the "safety" rear wheel drive chain driven bike. It was not until the bicycle design renewal in the 1970s that the idea of a direct-drive recumbent was seriously explored.

More recently Thomas Kretschmer in 2000 proposed and designed a direct-drive recumbent with a planetary gear hub for which he has German patents DE 19736266 and DE 19824745. John Stegmann in 2002 proposed a direct-drive design for cargo-carrying. In the following year the author built a direct-drive recumbent using a modification of a Schlumpf Speed-Drive unit.

Scope of the research

This research comprises a pedal force feedback analysis, a handling analysis, an experimental analysis, and conclusions with a recommended geometry.

Pedal force feedback

Since the pedals are mounted on the fork rather than the frame, the rider's pedaling force generates an alternating steering torque which the cyclist must resist. A reduction in this would result in a design that was more user-friendly for new riders and more comfortable.

Kretschmer suggested a shallow head angle to reduce the pedal force feedback. The shallow inclination aligns the head axis more closely with the direction of the applied pedal force, reducing the resulting torque about the steering axis. However this can have an adverse effect on handling. Therefore it would be useful to find the best compromise between low pedal force feedback and user-friendly handling.

Handling

In a direct-drive recumbent, the mass of the front assembly is considerably higher than with a regular bicycle and the centre of this mass is located further from the steering axis.

This increases the torque that is generated around the steering axis when the bicycle is leaned into a turn or when the steering is turned. This results in over-control, with more steering response than necessary for stable hands-free riding. To address this issue, a direct-drive recumbent requires a different frame and fork geometry. Kretschmer suggested 2-3 cm of trail (compared to about 5-6 cm in conventional bikes) and also a centering spring for the steering.


METHODS

PEDAL FORCE FEEDBACK ANALYSIS

The pedal force feedback is evaluated by using the pedal force data of Hull and Davis, 1981.  Their data is resolved around the steering axis to obtain the net torque around the steering axis caused by pedaling.  To translate the data to the recumbent position the concept of the recumbent angle (figure 2) is introduced.  The recumbent angle indicates the degree of inclination of the recumbent rider relative to a typical upright bike’s seat tube angle of 73 degrees.

Figure 2
Figure 2: Defining the recumbent angle — view larger


Determining the resulting force restrained by the hands of the rider

The force that the rider must exert to restrain the net torque around the steering axis depends also on the handlebar position.

Three handlebar positions are commonly used in recumbent bicycles: above-seat, below-seat, and hamster position.

Figure 5
Figure 3: Above-seat handlebar position

Figure 6
Figure 4: Below-seat handlebar position

Figure 7
Figure 5: Hamster handlebar position

The above-seat, arms outstretched position  (figure 3) allows the arms to be "locked" in the outstretched position, forming a mechanical brace between the seat back and the handlebar grips. This reduces the contribution required of the muscles in the arms, resulting in lower rider fatigue.

The below-seat position (figure 4) also allows the arms to lock in an outstretched position, but the plane of the outstretched arms is nearly parallel to the steering axis. As a result, the advantage of the mechanical brace of the outstretched arms is lost, and the arms will instead strenuously resist the pedal induced torque.

The hamster position (figure 5) lacks the bracing advantage of the outstretched arms, resulting in a greater contribution by the muscle groups in the arms, and correspondingly increased muscular fatigue.

Therefore, of the three possible positions, the above seat outstretched arm position is the superior choice for a direct-drive recumbent. This is also the handlebar position preferred by Stegmann.


HANDLING ANALYSIS

The handling of a bicycle arises from a complex interaction of gravitational, inertial and gyroscopic forces.

For a given head angle, the front wheel trail and the steering centering spring will determine how a direct-drive recumbent handles. At low speed, gyroscopic forces are low, and a static analysis of the applied gravitational forces on the steering can be used to set the front wheel trail and design an effective centering spring.

When a stationary bike is held vertically and the steering is turned from the centre, a torque is generated about the head axis (figure 6). A steering torque is also generated when the bike is leaned to one side with the steering held on-centre (figure 7). These two effects, which can be investigated separately, are known as steering-induced torque and lean-induced torque, respectively. Steering induced torque is also commonly referred to as "fork flop".

Figure 8
Figure 6: Steering-induced torque — view larger

Figure 9
Figure 7: Lean-induced torque — view larger

The steering-induced torque and lean-induced torque result from two applied gravitational forces: the force of the ground on the front wheel and the force due to the offset mass of the front assembly. "Offset mass of the front assembly" means that the centre of gravity of the front assembly (i.e. all the parts that swings with the steering) is offset from the head axis.

The design challenge is to reduce the steering-induced torque and lean-induced torque to a level that is similar to that of an upright bike. There are several ways of achieving this reduction.


The question of negative trail

Jim Papadopoulos in 1987 suggested that a bicycle with a large offset front assembly mass may benefit from some negative trail. With negative trail, the ground force on the front wheel produces a torque in a direction opposite to the torque coming from the offset front assembly mass, counteracting the effect of excessive front assembly mass and leading to a manageable torque for good handling.

The difficulty with this approach stems from the exclusion of all forces except gravity. Lateral forces also act on the front wheel due to uneven pavement, bumps and ridges. Since the resistance to these forces is inertial and, at higher speed, also gyroscopic, this produces a bike that may be quite stable on a smooth flat surface, but jittery and unsettling to ride on a rough surface.

Experiments with the variable geometry bike described below confirm this. A negative trail value that has this desired counterbalancing effect is about 60mm for a 56 degree head angle. The steering is well constrained on smooth turns, but the overall response of the bike is highly unfamiliar, particularly at low speed and on uneven surfaces. Therefore, in spite of the theoretical advantages of negative trail in controlling excessive front assembly mass, it is rejected because it lacks overall user-friendliness and stability.


The question of a counter-balance mass

Another way of balancing the offset front assembly mass is to add a counter-balance mass. This mass would have to be considerable, however, and therefore this idea is rejected also.

Determining trail and centering spring constant

Excluding these options, the trail and centering spring constant are determined by equating the steering-induced torque of a direct-drive recumbent to that of a reference upright bike.  This ensures that at least the fork-flop characteristics of the direct-drive recumbent will be similar to a regular upright bike—increasing user-friendliness.

EXPERIMENTAL ANALYSIS

The purpose of the experimental part of this study is to assess the calculated results qualitatively. To do this a variable geometry bike (figure 8) was constructed to test the head angles with the corresponding trail values and spring constants. The bike employs the wheels, seat, handlebars, brakes, and transmission of the author's bike of figure 1.

Figure 10
Figure 8: Variable geometry test bike

The frame of the variable geometry bike is constructed so that changes in head angle and trail do not affect the positioning of the major frame members, and so that the position of the rider on the bike remains unchanged. This is done by using a headset hinge (A) which can be located in a range of positions on the "down tube" of the frame. The down tube is, in fact, not a tube but rather it is composed of four plates: two upper plates (B) and two lower plates (C) which sandwich the respective hinge flanges. At the opposite ends the lower plates sandwich a flange attached to the main horizontal frame member, and at the upper end the upper plates surround a flange attached to the fork assembly. The plates are accurately machined and held to the flanges by shoulder bolts. Thus by changing the four plates both the head angle and the trail can be changed.

A torsion bar spring (D) is placed between the two top plates and the two bottom plates to act as the centering spring. It is generally hat-shaped, with the vertical parts, which are parallel to the head axis, acting as torsion bars. The active length is thus the sum of the vertical lengths.


RESULTS

Table 1 lists the input values for the direct-drive recumbent bike. These values are based on the variable geometry frame and may, of course, differ in a possible future production bike. Also the mass of the front assembly will probably be less than the measured 19.5 kg (including feet) with a production bike. It is unlikely, however, that the front assembly mass will ever be much less than 15kg for an adult rider. Measurements were taken from an actual rider, (male, 1.83m tall, 89 kg) so these will also vary.

Table 1: Input values for direct-drive recumbent bike

Head angle (from horizontal)variable
Radius of front wheel348 mm13.7 in
Fraction of weight on front wheel (bike and rider)0.5
Tread (lateral distance between pedal centers)297 mm11.7 in
Handlebar grip width (between grip centers)465 mm18.3 in
Seat height (defined as 76 mm (3 in) below hip pivot of rider)554 mm21.8 in
Distance from hip pivot to bottom bracket841 mm33.1 in
Crank length170 mm6.69 in
Plane of restraint of rider's arms (above horizontal)0.244 radians14 degrees
Mass of the front assembly (including rider's proportion)19.5 kg43 lbs
Trail28.6 mm1.125 in
Centering springnone

Table 2 gives the input value for the reference bike. The reference bike is not one particular bike, but a "generic" upright bike. It represents a typical upright bike to which the user is familiar.

Table 2: Input values for reference upright bike

Head angle (from horizontal)72 degrees
Radius of front wheel348 mm13.7 in
Fraction of weight on front wheel (bike and rider)0.4
Trail50.8 mm2.0 in
Seat tube angle (from horizontal)73 degrees
Mass of the front assembly3.64 kg8.0 lbs

PEDAL FORCE FEEDBACK ANALYSIS

Steering torque variation with crank position

The pedal force feedback varies as the crank rotates. Figure 9 shows a typical variation with crank position. The head angle is 62 degrees to the horizontal (author's bike - figure 1). Note that the zero degree position is when the right crank is aligned with the head angle, and facing downward and forward.

Figure 11
Figure 9: Torque vs. crank angle

Figure 9 indicates that the pedaling torque feedback to the handlebars follows an approximately sinusoidal curve, with a maximum value when the right pedal crank is oriented at about 120 degrees counterclockwise (CCW) from the inclination of the head axis. There is a considerable flat portion of the curve extending from 120 to 150 degrees. Since the head angle in figure 11 is 62 degrees to the horizontal, this range is from 2 to 32 degrees after the top vertical position in the normal clockwise sense of the rotation of the right crank.


Maximum steering torque due to pedaling

The severity of the pedal force feedback can be expressed as the maximum torque generated about the steering axis for each 360 degree rotation of the cranks. Figure 10 depicts this torque as a function of the head angle, when only the components acting in the plane of rotation of the cranks are included (in-plane only), and when all the components are included (all components). The out-of-plane forces are of a double benefit to the direct-drive recumbent designer: they reduce the force feedback and increase the effectiveness of reducing the head angle. This out-of-plane effect is predominately due to the outward lateral force which is generally in phase with the principal pedal force.The outward lateral pedal force arises from the direction applied by the rider's foot to the pedal. The line of this force passes through the center of pressure of the rider's body on the seat, creating an outward component at the pedals.

Figure 12
Figure 10: Peak torque vs. head angle

Figure 11 illustrates the peak torque around the steering axis expressed as a percentage of the peak torque applied to the crank axis. This gives a sense of how much of the torque required for propelling the bike is returned to the handlebars.  As shown, shallow head angles can reduce this to a little less than 20 percent.

Figure 13
Figure 11: Peak torque as a function of peak pedaling torque

Figure 12 depicts the peak restraining force per hand expressed as a percentage of the peak pedal force. This figure shows that the peak restraining force per hand can be as low as 13% of the peak applied pedal force. This underscores that riding a direct-drive recumbent is not a tug-of-war between the rider's legs and arms—the force transmitted back to each hand is about an order of magnitude less than that applied to the pedals.

Figure 16
Figure 12: Peak restraining force per hand as a percentage of peak pedal force


Comparing to other moving bottom bracket (MBB) bikes

It is instructive to compare the direct-drive recumbent with other recumbent bikes with moving bottom brackets (MBB). These other designs usually have a bottom bracket mounted generally above and in front of the front wheel, with a chain extending back to a front hub or derailleur gear. Examples are the Flevobike, Cruzbike™, Python (see Openbike (2008)), and bicycles developed by Tom Traylor (see for example United States design patent D277,744). Compared to a direct-drive recumbent, the steering axis is much further behind the pedals and thus the lateral outward pedal forces have a greater leverage around the steering axis, leading to reduced pedal force feedback. The distance from the steering axis to the bottom bracket can be in the range of 40-50 cm.

Figure 13 compares the pedal force feedback of two chain-driven MBB bikes with that of the direct-drive recumbent. The first chain-driven MBB bike is typical of a full size wheel (700C) configuration, with a steering axis to the bottom bracket distance of 47 cm. The large front wheel dictates a high bottom bracket and thus a recumbent angle of 73 degrees is typical (bottom bracket at hip pivot height). The second chain-driven MBB bike is typical of the small front wheel design, with a low bottom bracket giving a recumbent angle of 53 degrees and a steering axis to the bottom bracket distance of 40 cm. An above seat handlebar position similar to that of the direct-drive recumbent is assumed for both designs.

Comparing the curves in figure 13, a chain-driven MBB bike has a considerably lower (about one third) restraining force than a direct-drive recumbent, except in the very shallow head angle range where the poor leverage in the plane of the outstretched arms overrules.

Figure 20
Figure 13: Direct-drive compared to chain-driven MBB bikes


HANDLING ANALYSIS

Trail as a function of head angle

Figure 14 shows trail as a function of head angle as calculated. The trail of the front wheel varies very little in the head angle range of interest (52 to 62 degrees). This also agrees with the 2-3 cm proposed by Kretschmer (2000) for shallow head angles.

Figure 21
Figure 14: Trail vs. head angle


Centering spring constant vs head angle

Figure 15 depicts the spring constant for the centering spring as a function of head angle, as calculated.

The centering spring rate increases rapidly with decreasing head angle. For example, the spring rate required for a 50 degree head angle is double that of a 62 degree head angle. This illustrates the importance of a centering spring as the head angle gets shallower.

Figure 22
Figure 15: Spring rate vs. head angle


EXPERIMENTAL ANALYSIS

The results of the test runs are of necessity somewhat subjective. The rider is the author in each case. The test runs are done using the variable geometry bike (figure 8) with a front wheel trail of figure 14 and, except as noted, a centering spring rate of figure 15. The first test (62 degree head angle) is the author's direct-drive bike (figure 1) which has no centering spring and a trail of 28.6 mm (1.125 in). No clips or cleats were used.


DISCUSSION

Figure 16 presents a convenient way of visualizing the pedal force feedback results. As shown in the figure, the rider exerts a pedal force extending in an outward-V from the centre of pressure of the rider on the seat to the pedals. The angle of this V produces the outward lateral pedal forces. Clearly, the closer the steering axis is to the rider's centre of pressure, the lower the resulting pedal force feedback. This is due to the correspondingly smaller lever arm around the steering axis as the steering axis approaches the vertex of the V. Thus the goal of the designer is to minimize the distance L in figure 16. This is consistent with Openbike (2008), who imply that in order to avoid any pedal force feedback, the steering axis should be aligned between the rider's hip pivots. As can readily be seen, the distance L in figure 16 can be minimized by any of three ways: a) moving the steering axis further back (i.e. decreasing the trail); b) decreasing the head angle; and c) increasing the seat height.

Unlike other moving bottom bracket bikes such as the Flevobike, the direct-drive recumbent designer does not have the luxury of translating the steering axis back toward the seat to reduce pedal force feedback—this would produce too much negative trail. Instead the designer is left with the approaches above and also the option of increasing the handlebar width and reducing the tread. Therefore the practical limits of all these are critical to the design.

Figure 23

Figure 16: Pedal force path visualization — view larger

Minimum head angle

From the test runs, it is clear that 56 degrees is the minimum practical head angle for user-friendly riding. Further reduction slows the steering response and causes a handlebar motion that is inconsistent with the plane of the outstretched arms of the rider.

Maximum seat height

The maximum seat height is determined by two criteria a) the rider's feet must still be comfortably placed on the ground, and b) the centre of mass of the bicycle and rider must remain low enough for effective braking.

From the author's own riding experience, a compressed seat height of 56 cm ensures that the rider's feet can be placed on the ground without discomfort. Given the author's size (1.83 m tall, 0.841 m hip pivot to bottom bracket), this seat height corresponds to a recumbent angle of 53 degrees, where the compressed seat height is defined as 76 mm below the rider's hip pivot.

Therefore a recumbent angle of 53 degrees is considered to be a good compromise between rider comfort/safety and reduced pedal force feedback.

Maximum handlebar width

The author's direct-drive recumbent and the variable geometry bike both have a handlebar width of 465 mm between the handlebar grip centers. Given an inverted U or W handlebar design, this width could be increased to 560 mm without being unduly cumbersome. The inverted U or W shape allows the center of pressure of the hands to be further apart for a given overall width, and provides greater knee clearance.

Minimum tread

A tread value of 297 mm (centre-of pedal to centre-of-pedal) is based on an adaptation of a commercially available planetary chain ring unit (Schlumpf Speed-DriveŽ), so the tread is similar to that of a regular upright bike with a standard 68 mm wide bottom bracket. It is not really practical to reduce the tread to less.

Wheelbase

Kretschmer suggested a wheelbase of 1200 mm for a direct-drive recumbent, and Stegmann 1450 mm. The author's direct-drive recumbent has a wheelbase of 1524 mm, and the variable geometry bike one of 1475 mm. With the shorter wheelbases there may be traction problems on hills due to the lightly loaded front wheel.


CONCLUSION—RECOMMENDED DESIGN

Table 3 presents the recommended design parameters for a user friendly direct-drive recumbent, based on the results of this study.

Table 3: Recommended design

Wheel size700C front and rear
Wheelbase1300 to 1550 mm (51 to 61 inches)
Head angle56 degrees from the horizontal
Centering spring rate18 Nm/rad  (based on figure 15) and adjusted for particular rider
Trail of the front wheel25 mm (1 inch)
Seat height560 mm (22 inches) for 1.83 m rider
Recumbent angle53 degrees
Tread297 mm (11.7 inches) between pedal centers
Handlebar positionover-seat, arms outstretched
Handlebar typeinverted-U or inverted-W
Handlebar width560 mm (22 inches) between handlebar grip centers
Front assembly with high rigidity in torsion

This design returns only 12% of the peak applied pedal force to each hand of the rider.

The resulting bicycle is shown in Figure 17. 

Figure 24
Figure 17: Recommended design


ABOUT THE AUTHOR

Jeremy M. Garnet , M.A.Sc. is a mechanical engineer with Industry Canada.  His work in bicycle design is a personal interest.  He has been a member of the (I)HPVA since 1998 and lives in Ottawa, ON, Canada. He can be reached at: jeremy DOT garnet AT sympatico DOT ca 

REFERENCES

Hull, M. L., and R. R. Davis (1981). "Measurement of pedal loading in bicycling: I. Instrumentation." Journal of Biomechanics 14:843-855.

Davis, R. R., and M. L. Hull (1981). "Measurement of pedal loading in bicycling: II. Analysis and results." Journal of Biomechanics 14:857-872.

Papadopoulos, Jim. (1987). "Bicycle steering dynamics and self-stability: A summary report of work in process." Cornell Bicycle Project report, December 15; http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/papers/bicycle_steering.pdf

Kretschmer, Thomas (2000). "Direct-drive (chainless) bicycles.", Human Power, no. 49:11-14.

Stegmann, John. (2002). "Chain of thought." Velo Vision, no. 8:22-25 (December).

Fehlau, Gunner. (2003). The Recumbent Bicycle, 2nd ed. Grand Rapids: Out Your Backdoor Press.

Garnet, Jeremy. (2003). "Delving into direct drive." Velo Vision, no. 12:18-20 (December).

Wilson, David Gordon. (2004). Bicycling Science, 3rd ed. Cambridge, Massachusetts: The MIT Press.

Openbike (2008) http://en.openbike.org/wiki/Pedal/Steering_Interference.

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