Determination of hydrodynamic drag forces and drag coefficients on human leg/foot model during knee exercise

Abstract

Objective. The purpose of this laboratory experiment was to measure hydrodynamic drag forces in barefoot/hydro-boot conditions and accordingly, to determine the coefficients of drag on human leg/foot model during simulated knee extension–flexion exercise.

Design. The prosthesis of the human lower leg was set in a water tank and connected into an isokinetic force dynamometer to measure resistive forces during knee motion.

Background. Quantifying resistance for aquatic exercises has been a challenge in hydrotherapy. The use of models of foot/leg provides a practical method to calculate coefficients of drag and to estimate resistance for rehabilitation purposes in musculoskeletal and amputee patients.

Methods. The dynamometer produced constant angular velocities of 250°/s, 270°/s and 300°/s to the prosthesis. The baseline for measurements was performed in barefoot condition. A hydro-boot was used to study effects of increased frontal area (30%) of the leg on drag forces and coefficients.

Results. The maximal drag force values were 61 N (300°/s) in barefoot and 270 N (270°/s) in hydro-boot condition. Related drag coefficient values during the range of motion were from 0.3 to 0.1 and from 1 to 0.8, respectively.

Conclusions. Drag force and related drag coefficient were highest during the early part of extension (150–140° flexion) as the model was opposing the lift forces with the influence of water resistance. The effect of velocity was remarkable on drag forces but minimal on drag coefficient values.

Relevance

The drag forces and coefficients of this experiment can be clinically utilised to calculate hydrodynamic forces to develop progressive knee exercise programs as well as to design of prosthesis for amputee patients.

Introduction

In swimming research, laboratory experiments have been employed to measure hydrodynamic forces on human hand/arm models to better understand the relationship between the swimming man and the water environment. For the calculation of propulsion in freestyle swimming, drag and lift forces have been measured to determine the coefficients of drag and lift [1], [2]. In hydrotherapy, similar approaches are needed to analyse mechanical characteristics of underwater movements of human leg/foot and prosthesis. This kind of basic information is necessary to develop progressive water exercise programs for patients with lower leg disorders as well as effective aquatic exercises and well-fitted prosthesis for amputees [3].

An object moving through the water with a constant velocity, an additional resistance force due to fluid drag is acting on the object. The direction of the drag force is opposite to the moving line. The drag due to turbulence behind the object is referred to as pressure or form drag while the quantity of friction between the boundary layer of the water and the object is called surface drag [4], [5]. In addition, the drag force can be divided into passive and active drag. The former is the resistance by the water that an object experiences in an unchanging posture and the latter is the water resistance related to the swimming motion [6]. Passive drag can be measured by towing the swimmer through the water and drag forces (F_d) can be calculated by the general fluid equation [7]

$$\text{F}{}_{\mathrm{<mtext>d</mtext>}}\text{=1/2ρAv}{}^2\text{C}{}_{\mathrm{<mtext>d</mtext>}}\text{,}$$

where ρ is the fluid density, A the projected frontal area of the object, v the velocity and C_d the drag coefficient. According to the hydrodynamic principles, the force required to overcome the fluid drag is effected by the size and shape of the projected area. Additionally, the drag force is a function of the velocity squared, which means that the doubling of the speed quadruples the drag force. The coefficient of drag is related to the shape, streamlining and the Reynolds number of an object. C_d can be calculated if the total drag force is measured, for example, by force dynamometer [4].

The present laboratory experiment was designed to measure underwater resistive forces exerted during simulated knee extension exercise. The specific aims of this study were (1) to measure hydrodynamic drag forces in order to determine the coefficients of drag on human leg/foot model in barefoot condition and (2) to measure hydrodynamic drag forces to determine drag coefficients with hydro-boot condition in order to examine the effects of increased leg frontal area on drag forces and coefficients of drag.