SOURCES OF UNCERTAINTY
SOURCES OF UNCERTAINTY
UNCERTAINTY PERCENT CONTRIBUTIONS
GOALS OF UNCERTAINTY ANALYSIS
The goals of analyzing the sources of uncertainty is to assess how our power outputs are affected by uncertainty in our instruments and measuring techniques. Random and systematic uncertainties in the stopwatch and heart rate monitor used have been estimated and combined to give us a potential overall uncertainty in our experiment.
Table 1. Possible sources of error and estimated uncertainties in our heart rate monitor measurements.
Table 2. Possible sources of error and estimated uncertainties in our stopwatch measurements.
UNCERTAINTY ANALYSIS
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Figure 1- 3 shows the relative uncertainty for each subject's calculated power output of combined uncertainties for power by considering the uncertainties of different variables like time of sprint, time of day and individual velocity. We assume a 1 % error for velocity and mass due to rounding error and/or calculation error.
UNCERTAINTY IN EXERTION CALCULATIONS FOR EACH SUBJECT
UNCERTAINTY IN POWER CALCULATIONS FOR EACH SUBJECT
UNCERTAINTY IN POWER CALCULATIONS FOR ALL SUBJECT AT SPECIFIC TIMES
UNCERTAINTY PERCENT CONTRIBUTIONS OF EACH VARIABLE FOR EACH SUBJECT
UNCERTAINTY PERCENT CONTRIBUTIONS OF EXERTION FOR EACH SUBJECT
UNCERTAINTY PERCENT CONTRIBUTIONS OF EACH VARIABLE AT EACH POWER VALUE AT SPECIFIC TIMES
CONCLUSIONS FROM UNCERTAINTY ANALYSIS
Based on our uncertainty analysis, we found that the uncertainty of mass of individuals and time of day have very little impact on the overall uncertainty of power. This finding is interesting because we would expect to see a significant difference in power at different times of the day. For the most part, the uncertainty of time of sprint has the most impact on our data and velocity having little to no impact on the overall uncertainty. However, throughout the analysis, there are a few points in which we obtain huge uncertainties in velocity. We are unsure of the cause of it but it may be due to some errors in our calculation of velocity. All in all, we think that the uncertainty in the project is not too high however, there are certain instances in which we can find a spike in uncertainty especially the part related to power calculation
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The overall analysis of the contribution of each variable towards the overall uncertainty shows that the time of sprint is the main contributor to the uncertainty in our analysis but we found that there are instances where we would have a high uncertainty of velocity. Although it is uncommon but it does happen in at least once at each time of the day.
In analyzing the uncertainty of percent exertion for each individual over the whole data set, we found that the only contributor to the uncertainty is the uncertainty in percent exertion which makes sense because the only variable involved in the calculation is the heart rate of subjects after each sprint.
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Full Uncertainty Analysis Excel File
Figures 4 - 6 show the relative uncertainty of percent exertion for each data point obtained from each individual.
There are a few outliers in the data set. After examining the data, we found that the time of the sprint is the variable that causes the outliers considering the UMFs.
The relative uncertainty for the percent exertion for each subject is within the range of 4.0% to 5.5%. This consistency of data may be because the calculation for percent exertion only involves the heart rate of a subject after the sprint and the max heart rate without involving other variables.
The analysis of relative uncertainty shows a few outliers in the data set. After analyzing the data set, we found that the largest contributor to the outlier is the uncertainty in the time of sprint.
In analyzing the uncertainty percent contribution of each variable at each power value, we found that the time of sprint is the variable that has the largest impact on the overall uncertainty of the power value of each subject. However, there are instances when the uncertainty of velocity prevails and this may be caused by how the calculations work out during data analysis.
Figures 17-20 show the uncertainty percent contribution of each variable at each power value in the experiment for all subjects at each of the four times of the day.
Figures 14-16 show the uncertainty percent contributions of heart rate at each percent exertion value in the experiment for each individual
Figures 7-10 show the relative uncertainty of power in the experiment for all the subjects at each time of the day.
Figures 11-13 show the uncertainty percent contribution of each variable at each power value in the experiment for each individual subject.
