# Pilgrimage Part 2 - Effort

#### Overview of the Cruise

I looked at the speed of Perseverance with respect to the motor input power (i.e. the electrical power input to the motor controller, not the mechanical power on the propeller shaft). This analysis was carried out plotting the “effort” (power/speed**3) along each section of the pilgrimage. This diagram shows that the effort varied significantly during the cruise, with spikes where the boat was manoeuvred through locks or shallow water, and less power for example going downstream. This view is from the south, with the Wey in the foreground, the Basingstoke next then the Thames and the Oxford in the background and the Grand Union on the right.

#### Condensing the Data

To examine this further, and try to quantify the variation, periods of steady cruising were defined as speed changes of less than 0.4 mph per minute, and power changes of less than 0.6 kW per minute. Periods where these conditions were both met for at least two minutes were then extracted and the average speed and power computed. The periods were weighted by the overall time on condition.

The route was broken into navigation segments, the Oxford Canal in brown, Thames in lilac etc. The Wey navigation was segregated into upstream and downstream conditions, and the tidal Thames and upstream on the river Brent separated. The flow on the Grand Union where it joins with other rivers was not considered significant, both because the flow was not apparent during the cruise and because the effect will be masked by the large number of measurements on the canal proper.

#### Power Curves

The data was simplified by assuming a function with only two parameters, a power coefficient and a flow velocity.

`Electrical Power = k x (U – flow)**3`

For each __canal__ section of the cruise, the flow was identified as zero and a power coefficient was computed, and for __river__ sections the power coefficient was estimated from the type of river, then the flow velocity calculated.

Here is the data for the Grand Union, showing how the data points for speed and power are mapped onto a single cubic curve through zero:

On river sections, I used a cubic coefficient representative of that scale of waterway and estimated the river velocity. For example, our short journey from Teddington to Brentford started at the peak of a neap tide with no apparent flow at Teddington. As novices we were surprised at the significant tidal flow downstream by the time we reached Brentford. This chart shows all the fitted curves:

This analysis has been extended by adding two extra pieces of data, namely the results of the original Ortomarine trial on the Droitwich canals and some precise measurements taken on the Grand Union stretch outside Ventnor marina (which is straight and wide).

For Perseverance, the base coefficient, k, comes out extremely close to 0.1. I therefore modified the coefficients to be k/0.1 for ease of interpretation.

#### Results

Coefficient Flow (mph)

Grand Union Canal Outside Ventnor marinas 1.0 0

Droitwich Canals 1.2 0

Grand Union Canal Hanwell to Norton Junction 1.3 0

Oxford Canal 1.5 0

Basingstoke Canal 3.3 0

Wey Navigations 1.2 0.2

River Brent 1.2 0.6

Thames 1.0 0.5

Tidal Thames 1.0 0.8

Clearly the river flow velocities only apply to the days that we were cruising those rivers, and in the case of the tidal Thames from Teddington to Brentford, the time of the tide (we were on a neap tide, starting right on the top of the tide).

What does this mean? If your boat uses a certain amount of power to travel on a wider section of the Grand Union, then to travel at the same speed on the Oxford Canal will need 1.5 times that power. Someone who cruises using 10 hp to do 3.5 mph downstream on the Thames will need 33 hp to do 3.0 mph on the Basingstoke.

#### Conclusion

The outstanding item in this table is the high coefficient for the Basingstoke Canal. Cruising this waterway at a given speed takes more than twice the power of any other canal. This was primarily due to the shallowness of the canal. In fact, the canal was closed to new visitors the day we left. There was also hindrance due to weed, but we were diligent in removing weed whenever we were aware of its presence, so this data is representative of anyone cruising the canal.

Data from electric boats can be used to help navigation authorities decide where to carry out dredging operations most effectively.