An Analysis of the Fitz Water Wheel at Falls Mill
by
Stephen Moss
This article discusses an analysis performed of the 32' overshoot steel Fitz water
wheel operating at Falls Mill near Huntland, TN. The analysis was one part of a larger
effort to develop a dynamic computer simulation of the entire mill. This portion is
presented here due to its general applicability to Fitz style water wheels.
The purpose of the analysis was to determine the amount and center of gravity of
water in a water wheel bucket filled to capacity for any angle around the wheel. This
was necessary for the force and moment calculations in the mill simulation. The data
on the wheel was obtained primarily from Dr. John Lovett, the owner of Falls Mill, and
from measurements on the wheel itself. Further information was obtained from a
previous set of three Old Mill News articles by Mr. Robert L. Omland entitled "The
Modern Steel Overshot Water Wheel."
The following Figure 1 is a diagram of the wheel with measurements pertinent to this
analysis. The wheel contains a total of 112 buckets, and the dimensions of each are
provided in Figure 2. The x and y coordinates of this bucket are referenced to the
center of the wheel, with the tip of the bucket being directly above this center. Again,
these are dimensions which were directly applicable to determining the maximum
weight of water in the bucket at any given angle, and are clearly not suitable for
machining purposes. Each bucket is 47 5/8" wide.
Figure 1 -- A Diagram of the Wheel at Falls Mill
Figure 2 -- A Diagram of an Individual Fitz Style Bucket of the Wheel
Figure 3 is a plot showing the results of the integration. The calculations were
performed only for the side of the wheel traveling downwards, i.e., assuming that the
water is not injected prior to top dead center of the wheel. The solid line is the
maximum capacity in gallons of a single bucket as a function of angle in degrees
around the wheel. It is indicative the point at which a bucket will begin to spill water.
For example, a bucket filled to 11 gallons will hold its water to the 120° mark. Over the
next 20°, it will spill 4 gallons of water. The Fitz design bucket will hold no water
beyond 170°, and begins to dump rapidly after 155°. This graph does not, of course,
consider the effect of the two holes allowing water to flow from a higher bucket to the
lower one. These were placed in the buckets for starting purposes, and to prevent a
vacuum from stopping the wheel if a flood raised the discharge level above the wheels
lower rim.The dotted line is the torque in ft-lbf produced by this bucket, filled to its
maximum, as if all the weight of the water were concentrated at its center of gravity. An
integration of the area under the maximum torque provides a value representing
maximum torque producible by the wheel if all the buckets are holding their maximum
amount of water, and has a value over 180,000 ft-lbf-deg. This is over 1/2 ton of force
applied to a lever arm 1 foot long for each degree of travel around the wheel!
Figure 3 -- The Results of the Bucket Capacity Integration
For application of this graph to other water wheels, the X-axis (gallons) is linearly
scalable as the width of the bucket decreases, and the effect of varying the diameter of
the wheel on this axis will be small so long as the spacing of the buckets is not
significantly altered.
Falls Mill is operating today, producing stone-ground grains. It is constantly being
maintained and restored, and is open to the public.