Dynamometers: Measuring Wave Forces

Measuring the hydrodynamic forces or water velocities beneath breaking waves is a difficult task. A simple way to find the maximum forces and velocities that a location has experienced is to use these mechanical dynamometers. Much like the maximum-recording spring scales used to measure fish, these provide a single measurement of the largest force experienced by a test ball since the last time they were read.

These devices are robust, inexpensive and simple to construct. The following pages will explain how to build and use them.



Rods needed to build Dynamometer
  • CPVC (Chlorinated Polyvinyl Chloride) schedule 40 pipe (below left), 6 ½" per dynamometer. The nominal pipe size is advertised as 3/8". It has an outer diameter of approximately 0.63", a wall thickness of 0.075", and an inside diameter of approximately 0.48", which will be bored out to accomodate the 0.5" diameter delrin plugs.  CPVC was sold for hot water piping, but is getting hard to find these days since it's mostly been replaced by PEX in home plumbing applications.  Please note that ½” PVC tubing is a different size and won't do.
  • ½” Black Nylon molybdenum filled rod (below right) 5/8" per dynamometer. Available from Small Parts Inc.  (part number O-ZRNY-8) or from McMaster-Carr (part number 8554K1).
  • ½” Delrin Rod (below center) 3/4" per dynamometer.  Available from Small Parts Inc. (part number O-ZRD-8) or from McMaster (part number 8572K55). 



  • PVC ½” Threaded female coupling collar (below center); these come in a dual threaded female coupling form. These are regular PVC, not CPVC.  Available at hardware stores. 
  • PVC ½” threaded male coupling (below left). These are regular PVC, not CPVC. Available at hardware stores.
  •  8-32 x 5/8” stainless-steel (or brass) machine screw (below right).  Available at hardware stores or McMaster-Carr.


  • 1” diameter Polypropylene balls (below left). Available from Small Parts Inc. (part number O-BPP) and from McMaster-Carr (part number 1974K24)
  • Wiffle Balls (practice golf balls).  Available at golf stores. (below right).
  • Epoxy glue (not 5-minute epoxy).
  • Multi-purpose PVC, CPVC, and ABS cement and purple primer for PVC and CPVC.  Available at hardware or plumbing stores.
  •  Izorline 130 lbs test dacron fishing line (right).  Note:  It is our experience that monofilament or thin metal lines are not long-lasting enough for this purpose.

  • Extension springs (right) 0.36" diameter spring, 3.0" long, spring constant 2 N/mm, stainless steel.  Available from Associated Spring/Raymond (part number E03600583000S)
  • Sheet rubber (ours is scrounged from old truck innertubes) to be cut into small pieces (right).
  • Cut the threaded female couplings in half on a band saw (below).  These are the dynamometer collars that are stuck into intertidal rocks using marine epoxy.      
pipe being drilled
  • Ream out the collar threads using a ½” – 14npt tapered tapping bit (above right).  These couplers have a tapered thread, by re-threading them past the taper so they have a straight thread makes it easier to place meters in and remove meters from the collar.
tool with wrench


  • Cut the female half off the threaded male end coupling/female coupling (see below).  Leave the hex nut shoulder on the male threaded end.
person holding pipe
  • Cut the Delrin Rod (white) end plugs into ¾” lengths. The metal sizer (below right) shows one method of efficiently cutting equally sized pieces. Below center shows the metal sizer in use.
  • Cut the Molybdenum Filled Nylon Rod (black) guides into 3/4” lengths.
  • Cut the CPVC tubing into 6 ½” lengths (below left).
  • Drill down the center of the Molybdenum string guide, using a 0.199 #8 bit (slightly bigger than nose of router bit).  Use a lathe so that the holes are accurately centered (below left).
  • Hollow out a cavity in the center of the Delrin end plugs.  Use a bit that is a slightly larger diameter than the spring (u 0.368"), such as a 0.377" bit.  Leave approximately 1/16" of material at the bottom end of the plug to seal out sand in the field.  

    This operation is best carried out on a lathe so that the holes are accurately centered

     (above right).
  • Bevel the top end of the string guide using a quarter-round router bit (below left).  The router bit has a 1/4" shank, 5/8" diameter and rounding-over bit with no ball bearing on the head.  Remove sharp edges from the string guide.
  • On the lathe, turn out the inner diameter of the CPVC shafts just enough for a press fit with the end plugs and string guides (above right).  This can be done either with a standard boring bar on the lathe, or using a reamer of the correct size. A suitable reamer would be a 0.5010" oversize reamer available from McMaster-Carr (part number 3087A37).
  • On the lathe, turn out the inner diameter of the CPVC shafts just enough for a press fit with the end plugs and string guides (above right).  This can be done either with a standard boring bar on the lathe, or using a reamer of the correct size. A suitable reamer would be a 0.5010" oversize reamer available from McMaster-Carr (part number 3087A37).
  • Insert the Delrin rod end plug into the dynamometer shaft, with the hollowed out cavity facing upward (above right).  Drill a hole (using a size 29 = 0.136” diameter bit) 3/8" from the bottom end of the dynamometer through the shaft and the end plug (below left).  
  • Countersink one side of the hole, so that the screw will sit flush with the shaft (below right). 
  • Tap the hole for the 8-32 5/8” screws.  This is the screw that holds the spring in place. 
  • Use all-purpose PVC cement and purple primer to glue the threaded male coupling head onto the CPVC shaft, with the threaded portion facing down towards the bottom end of the shaft (above right).  (Put glue on each surface being glued together).  Make sure the flat top of the threaded male coupling head is flush with the end of the shaft.  Note:  CPVC glue does not glue PVC and vice versa.  Make sure to use all-purpose glue that glues both.
  •  Mill out a 3 1/8” by ¼” window (above left) in the side of the dynamometer (long enough to see the top loop of the spring and the bottom edge of the black string guide). You'll need to cut into the threaded portion of the dynamometer head for this.  Therefore, it is important to do this step before gluing the black string guides in place (since they are used for a measurement reference point). 
  •  Glue (with epoxy) the string guides into the top of the dynamometers so they are flush with the top of the CPVC and male threaded coupling (above right).
  • To roughen the polypropylene balls, use the lathe to cut 5 parallel grooves ~1mm deep into their surface (above left).  Drill a hole through the ball to thread the string.
  • Cut rubber stopper pieces (above right).  Make them big enough so they do not slip through string guide hole, yet small enough so they don't rub against the inside walls of the shaft (approximately 7mm square).

Text Alternative for Assembling a Dynamometer

Step 1: 

Tie the ball into the fishing line

Step 2:

Thread the fishing line through the string guide.

Step 3:

Use forceps to thread the rubber stopper.

Step 4: 

Push rubber stopper into place. 

Step 5:

Thread fishing line through top loop of the spring.

Step 6:

Tie string onto the spring, and pull the knot tight.

Step 7:

Use the lighter to cut the fishing line. The ends of the line will not fray if they are burned.

Step 8:

Pre-stress the meter to tighten knots.

Directions to upload dynamometer
Field Set Up

Drilling Holes:​

  • Drill Holes in intertidal rocks using a Chicago Pneumatic CP9A drill.  Drill a 5/8” diameter hole at least 7" deep.  Then widen the opening of the hole, as deep as the collar, using a 1 ¼” bit.  Center this second hole on the 5/8" hole and make sure it has the same orientation. 
  • Pack marine epoxy around the collar and surrounding rock being careful not to glue the dynamometer in place. 

  • Use a turkey-baster to flush out the holes after drilling.  Screw a dynamometer into its collar and glue the dynamometer with collar into the hole using marine epoxy (see below left).  (Placing the dynamometer in the hole in this fashion will properly orient the collar).  

  • After you remove the dynamometer, keep the hole capped using a 1/2" threaded male plug (pictured above on the right) to prevent the hole from filling up with sand or intertidal animals. 

    Dynamometer cap on rock

Recording Data from the Meters:

  • To read the meters take a measurement, with calipers, from the exposed bottom of the string guide to the rubber stopper.  Make a record of the number of the meter, the hole it was located in, and the measurement in mm.  Reading the meter is shown in the photograph below

Picture of dynamometer being measured

    In order to collect wave force data that can be compared to other data and converted into water velocities, it is necessary to calibrate the springs, and to convert the data using equations provided by Bell and Denny (1994).

    Dynamometer Spring Calibration

    Though the springs are manufactured to specific tolerences, it is important to verify the stretch and initial load constants for each spring.  Pre-stress the dynamometer (see below), before measuring the extension lengths, to tighten the knots in the string. 

    To calibrate a spring, hang each of five known masses from the meter containing the spring, and measure the resulting extension of the spring the same way you would measure the meter in the field (see Field section on reading meters).  Multiply masses by the acceleration due to gravity (9.8m/s2) to convert to units of force (N).  Fit the force and extension measurements to a linear regression:

    F = kx + c

    Where k is the spring constant, and the constant c reflects the force required to overcome the initial compression of the spring.  We have found that the spring constant does not seem to change significantly after spending time in the intertidal.

    To calculate forces for the meters with small polypropylene balls, divide these wave force numbers by the ratio of the area of a polypropylene ball to that of a wiffle ball. (Note: area refers to the area an approaching wave faces: if the diameter of the ball is 1” then the area is π(1/2)2 = 0.7855).

    Data Translation

    To use the extension measurements to calculate max water velocity (U) use the following equation from Bell and Denny (1994):

                U = ((kx + c)/a)(1/b)

    Where a and b describe hydrodynamic properties of the particular ball on the dynamometer.  Best estimates of a and b for wiffle balls from Bell and Denny (1994) are 0.575 and 1.93 respectively.



    Bell, E.C. and M.W. Denny. (1994) Quantifying "wave exposure": a simple device for recording maximum velocity and results of its use at several field sites.  J. Exp. Mar. Biol. Ecol. vol. 181:9-29

    Denny, M.W. and D.Wethey. (2000) Physical processes that generate patterns in marine communities. Chapter 1 in M. Bertness, M. Hay, and S. Gaines (eds.) Marine Community Ecology, Sinauer Press, N.Y.



    Small Parts Inc.    http://www.smallparts.com

    McMaster-Carr      http://www.mcmaster.com

    Associated Spring Raymond  http://www.asraymond.com