| Sumario: | While Velocita Ascensionale Media (VAM) can predict performance on steep hills, no such metric for flat terrain exists. Cyclists instead rely on power meters and estimates of air density, drag-area (CDA), and coefficient of rolling resistance Crr to predict ideal speed (IS): the speed they can maintain on a flat windless road. We propose a new parameter-free metric, Equivalent Speed (ES), to predict IS given just speed data. Unlike average speed, V, ES (the distance-weighted average of speed, ν) approximates IS closely. ES assumes constant CDA on a closed loop course. Average drag is proportional to ν², so on a closed course in the absence of wind or braking and ignoring the constant energy lost to rolling resistance, power is given roughly by P∝ν2V. An approximation to third order changes in speed about ES is P∝ν³. Since IS is defined to be constant, VIS=νIS and we find in this case PIS∝VIS 3. ES is then the solution to P=PIS for VIS. PURPOSE: To test the accuracy of ES in different conditions. METHODS: A standing start, out-and-back 40km time trial with 4 total sinusoidal hills is simulated. The following parameters are used. Frame mass: 7kg, wheel mass: 2kg, Crr: 0.0035, CDA: 0.25m², air density: 1.225 kg/m³, braking force: 200N. Hills of 0% (flat), 2%, 5%, and 10% gradient are tested. Both direct headwinds and crosswinds of 0m/s, 2m/s, 4m/s and 6m/s are tested on the flat course. Rider mass is 50kg, 75kg, or 100kg on the 2% course, but 75kg in the other tests. Rider power is 200w, 300w, or 400w on the 2% course, but 300w in the other tests. RESULTS: On the flat course the standing start and turnaround portions cause ES to incur an error (IS-ES)/IS=0.43%, where IS=12.17m/s. This error is mostly due to the start and turnaround (1.28% energy loss). ES incurs errors of 0.32%, 0.40%, and 0.42% for the 50kg, 75kg, and 100kg riders, with errors of 0.21% and 0.46% at 200w and 400w. ES incurs errors of -0.88% and - 7.1% on the 5% and 10% climbs. Speeds of twice IS are achieved on the 10% descent: too large for the third order approximation. Errors of 0.18%, -0.59% and -1.9% result from 2m/s, 4m/s, and 6m/s headwinds, with errors of 0.86%, 2.1%, and 4.0% in the respective crosswinds. CONCLUSIONS: Without a power meter or flat roads, ES can predict IS using just speed data. Error is less than 1% except on descents steeper than 5%, or in headwinds over 4m/s, or crosswinds over 2m/s.
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