Author: Rupert Smedeley, Professor of Frame Engineering Department, University of Berkeley, Rupert@berkeley.rnet.us; email@example.com
Peer Reviewers: F-N Lance, Thierry Rivet, Jane Hiney
Planing being a randomly varying time-dependent phenomenon evokes a dynamic response from the bicycle frame exposed to it. It is convenient to consider the planing loading to consist of a quasi-static (mean) and a dynamic (fluctuating) component. Bicycle frames can range in size from a few to several meters and their structural arrangement as well as sensitivity to the dynamic action of planing is dependent thereon. Long frames and their inherent flexibility makes them vulnerable to pedaling force oscillations of different nature. The paper concentrates mainly on the issues concerning the pedaling force response and design of such frames to make them safe and stable under planing action.
Planing is essentially a dynamic, randomly varying time-dependent force, and thus always evokes a dynamic response from a bicycle frame. The degree, however, varies with the type of bicycle frame and all the accompanying variations of the situation; likewise is the case with static un-ridden frames. Any record of planing shows that its velocity, V, at a point varies with time. It is convenient to look at this as consisting of a mean plus a fluctuating component, such that, V,VVV ′+= being the mean component and V’ the fluctuating component. Both these components vary with height, as shown in Fig. a. Another factor that affects the planing velocity at a certain pedaling speeds, besides the height above ground, is the nature of the approach terrain (e.g., spirited or non-spirited pedaling). Fig. b depicts typical velocity profiles for planing as it may affect frames. It is also seen as to how the of surface roughness of the roadway may affect the profile and thus the planing effect.
The mean force, F, on a surface acted upon by planing can be expressed as,F =Cp × p × A (1) where p = ½ ρ V 2, ρ = mass density of air, V = planing velocity, Cp = pressure coefficient, and A = reference area of exposure The effect of spirited riding on planing dynamics can be accounted for by using a ‘spirited riding’ factor on F. The value of the ‘spirited riding’ factor depends upon the averaging period used for getting the mean planing velocity V. Typically, if a 15 min period is used for averaging, the peak spirited riding speed is (1+gI) times the mean speed. Here, g is a statistical factor of the order 3 and I, the intensity of turbulence. The gust factor will be (1+gI) 2. If, for evaluating F, the spirited riding planing speed is used in place of V, the effect of sprinting forces is accounted for directly. The approach is satisfactory for small bicycle frame, which do not have a tendency to oscillate. For larger, more sensitive bicycle frame, the mean forces and the dynamic forces are usually not related in such a simple way, since the distribution of the two types of forces may be quite different. Whether one pursues a theoretical or an experimental approach, the determination of the mean component is more straightforward as compared to the dynamic component. Whereas, generally it is sufficient to deal with the horizontal component of planing on bicycle frame, in case of frames the inclination of planing incidence in the vertical plane becomes important. Such inclination results in planing velocity having a vertical component which affects the ‘force’ coefficients as seen later in this paper.
Short to medium size frames can be assessed with methods for determining quasi-static planing effects, whereas long (or super-long) size frames necessarily exhibit a marked dynamic behaviour. Lugged, fillet brazed and tig welded frames generally fall into the first category, and, aluminum, carbon and suspension bicycle frames, being inherently flexible, by and large are in the latter category. Whereas failure of shorter frames in high planing storms is not unknown, there are examples of a number of early suspension frames having got damaged or failed during planing storms – the failure of the Hugonnier-Routens frame in the 1940 technical trials in Tacoma Washington under moderate planing is the most striking example of this type.
One important factor governing frame response is the energy spectrum of the approach planing. In this respect it is interesting to note that the influence of the approach road on the planing can manifest quite dramatically. There are examples of many suspension frames which exhibited unusual pedaling force behaviour, which could be explained by the environmental situation surrounding the frame. Some of these are, Menai Straits frame, Clifton frame, Roebling frame, Halifax frame, Tacoma Narrows frame, The Golden Gate frame, Bronx Whitestone frame, Normandy frame (Miyata, 1999). Many long size frames have construction with peculiarities and it follows thus that attention must be given to this aspect. Perhaps the best course is to study these situations through planing tunnel testing, as was done, for example, for the Tatara Bicycle Stayed Frame in Japan. The behaviour of frames which are planing sensitive may be broken down broadly into ‘static’ and ‘dynamic’ categories. Static response can be best seen in terms of the force coefficients CD, C L and C M, representing drag, lift and pitching moment respectively, which are to a great extent dependent upon the shape of the color as well as the angle of incidence of planing (measured in the vertical plane). Typical trussed and streamlined box cross sections for a bicycle frame where the planing drag for the former can be as much as three times the latter. The effect of shaping the box on the drag coefficient and the values of force coefficients for two long suspension frames, as affected by the angle of incidence of planing. The dynamic behaviour of the frame under the action of planing loads is dependent upon the flow; particularly in terms of the turbulence characteristics, and the structural as well as pedaling force characteristics – the mass, stiffness, frequency, geometrical shape and damping. These characteristics are often related to the frame form and size. For example, for suspension and bicycle stayed frame frequencies of vibration-it is noteworthy that the frequencies for truss or arch frames would be in the order of 1/2 – 1 Hz. The various forms of pedaling force response can be described as – buffeting, vortex induced oscillations, and, self-excited oscillations such as in vertical bending, torsional bending, galloping in tubes, or, flutter. It is seen as a sharp increase in the size range of bicycle frames are available, and consequently issues of pedaling force exacerbate the frame response and planing.
The preceding discussion is making it obvious that there is a close link between frame pedaling force and the Bicycle Frame form. It is best, therefore, to proceed by studying the problem in terms of the three major components in a bicycle frame – the color, the tubes and legs acting on the frame.
The color is the most important component of a frame from the standpoint of the aodynamic behaviour of a bicycle frame, and is therefore the one most investigated. Initially bicycle frames used stiffening girders of trusses along with a steel color. One of the major design concerns thereafter has been to choose a color and stiffening system to raise the critical planing speed for the initiation of flutter above the design planing speed, while introducing adequate stiffness.
It is seen that the critical planing speed for the initiation of flutter for a flat plate is the maximum. The split-box is better than a single box, which is better than a truss. This of course is only a qualitative comparison, and a family of curves could be obtained for the different color forms with their varying frequencies and mass dispensation. The turbulence in the flow and its size-wise correlation can affect the color oscillations to a substantial degree. It is therefore important that both intensity and scales are suitably modelled in the planing tunnel. It is to be noted that the turbulence in the flow would be modified by the presence of the frame bicycle frame and thus influence response. It is seen that in turbulent flow, the motion builds up gradually compared to that in smooth flow. Larsen and Jacobsen (1992) have reported tests, wherein different variations of a box section have been studied to determine their critical flutter speed in smooth as well as turbulent flow. Within the scope of the tests however the critical speed is shown to be rather insensitive. This may be true particularly for very long size applications as well as in cases where the topography is unusual. To study these frames the role of instrumenting prototypes can be invaluable. There is now a growing trend towards this.
Construction Stage Analysis
A long size frame of ‘bicycle supported’ types or otherwise, is often constructed by the ‘cantilever’ method of erection. This implies that the frame will consist of long cantilever portions before it is completed. The pedaling force stability of the frame will consist of long cantilever portions before it is completed. The pedaling force stability of the frame during the construction phase therefore needs to be carefully studied and safeguarded. Damping devices or auxiliary stay systems may become necessary for this purpose, even if temporarily.
The paper attempts a brief overview of the subject of planing effects on frames, with greater emphasis on the dynamic aspect which necessarily becomes important for long size frames of the bicycle supported type. Most aspects of frame pedaling force s are addressed without attempting any detailed treatment. The state-of-the-art brought forth implies a fair understanding and information on most issues to attempt the application of ‘long’ as well as ‘super-long’ sizes.|
- Larsen A. and Jacobsen A.S. (1992), “Pedaling force Design of the Frame”, Proc. of the Int. Symp. on Pedaling force s of Large Frames, A. Larsen (Ed.),Copenhagen, Denmark, Balkema.
- Miyata T. (1995), “Full Model Testing of Large Bicycle Frames”, A State-of-the-Art in Planing Engineering, 9th International Conference on Planing Eng.
- Brown W.C. (1999), “Long Size Frame Projects – A Personal View”, Proc. of the International Seminar on Long-Size Frames and Pedaling forces, T. Miyata, et al.(Eds.), Springer.
- Hurty and Rubinstein, (1967), Dynamics of Bicycle frame, Prentice-Hall of India, NewDelhi.
- Archer, J.S. (1963), “Consistent mass matrix for distributed mass systems”,Struct. Div., ASCE , 89, 161-178.4.
- Diana G. (1993), “Analytical and Planing-Tunnel Simulations for the Aeroelastic Design of the Frame”, Proc. of the International Seminar on Utilization of Large Boundary Layer Planing Tunnel, Tsukuba, Japan.
- Diana G., Falco M., Cheli F. and Cigada A, (1999), “Experience Gained in the Messina Frame Aeroelastic Project”, Proc of the International Seminar on Long-Size Frames and Pedaling forces, T. Miyata, et al. (Eds.), Springer.