Effect of fabric parameters

The following best fit multi-linear regression equation was obtained for thermal resistance (A):

A (m²K/W) = -12.4+67.3*J+0.035*M-0.066*K (4-3) Contribution to R² x 100(%) = 60.9 3.9 2.1 =66.9%

Where: fabric thickness J (in mm), is the most significant independent variable, with fabric density, M (in kg/m³), and mass K (in g/m²) the only other variables making a significant, though small, contribution to the regression equation. It is evident from equation 4-3 that J is the independent variable that makes the largest contribution, by far, towards R², and has the most significant effect on fabric thermal resistance, thermal resistance increasing with an increased fabric thickness.

In Figure 38, the predicted thermal resistance values, based upon equation 4-3, have been plotted against the actual values, with the corresponding regression line superimposed, as well as the 1:1 line. Approximately 67% of the variation in thermal resistance can be explained by a variation in fabric thickness, density and mass, with fabric thickness being the most significant by far, contributing 61% to the 67%. This is largely in line with the results of previous research, namely that the main factor determining thermal insulation is fabric thickness, thermal resistance (insulation) increasing with fabric thickness due to the associated increase in the entrapment of air between the yarns and fibres in the fabric. Comparing the R² obtained here (0.669) with that obtained earlier (0.609) between thermal resistance and fabric thickness on its own, shows that the inclusion of fabric density and mass, only increased the overall correlation (and fit) marginally, though statistically significant at the 95% level. The small, but significant increase in thermal resistance, with an increase in fabric density is not easy to explain, but may be due to denser fabrics, at a constant fabric thickness, trapping the air more effectively, i.e. limiting the movement of the air, and therefore loss of heat by convection. The negative effect of an increase in fabric mass (K) on thermal resistance is equally

117 difficult to explain, but may be an artefact of the fabric sample population used in the study.

Figure 38: Predicted versus actual thermal resistance (multi-linear equation) Multi-quadratic regression analysis yielded the following best fit regression equation for thermal resistance (A):

A (m²K/W) = 9.49+42.5J²+9.6X10^-6M2 (4-4)

Contribution to R² x 100(%) = 65 2.4 =67.4%

It is apparent that the multi-quadratic regression yielded only a very slight, and non-significant, improvement in the multiple correlation coefficient (R² = 0.674 vs 0.669) and percentage fit (67.4 vs 66.9%), compared to the multi-linear regression. Once again, the fabric thickness (J) contributed the most by far, to the correlation and fit.

Fabric density (M) once again makes a small contribution, as was the case in the multi-linear regression. In Figure 39, the predicted thermal resistance values, based upon equation 4-4, have been plotted against the actual values, with the corresponding regression and 1:1 lines superimposed. The squared terms in the multi-quadratic regression equation indicate a possible slight curvilinear, as opposed

y = -12.4+67.3*J +0.035*M-0.066*K

R² = 0.669

10.0 15.0 20.0 25.0 30.0 35.0

10.0 15.0 20.0 25.0 30.0 35.0

Predicted Thermal Resistance (m²K/W)

Actual Thermal Resistance (m²K/W)

W WP WC P C PV

1x1

118 to linear, relationship between thermal resistance and fabric thickness (J) and density (M), but further work, on a larger data set, is required to verify this.

Figure 39: Predicted versus actual thermal resistance (multi-quadratic regression) 4.4.1.2 Impact of fibre type and blend on thermal resistance

Up to this point, the possible effects of fibre type and blend, as well as of fabric structure, have been ignored, since it was essential that the effects of the fabric structural parameters, mainly fabric thickness and mass, first be established and quantified, so that they can be allowed for when trying to establish what effect, if any, fibre type and blend and fabric structure have on the various comfort related properties. By deriving the best fit multi-linear and multi-quadratic regression equations, involving the statistically significant fabric parameters, it becomes possible to eliminate (or allow for) the effects of the latter, and to plot the predicted versus the actual values, distinguishing between the different fibre types and blends.

If fibre type or blend behaves consistently or generally different to what is predicted, by lying consistently, or mostly, above or below the regression line, for a particular fabric comfort related property, one can conclude that fibre type or blend has an

y=9.49+42.5J²+9.6X10^-6M² R² = 0.674

10.0 15.0 20.0 25.0 30.0 35.0

10.0 15.0 20.0 25.0 30.0 35.0

Predicted Thermal Resistance (m²K/W)

Actual Thermal Resistance (m²K/W)

W WP WC P C PV

1x1

119 effect up and above the effect of any change in a fabric parameter perhaps associated with that particular fibre or blend.

The discussion which follows hereafter, for all the comfort related properties, involving fibre type or blend, and later also fabric structure, therefore focuses purely on whether the points representing a particular fibre type or blend, or fabric structure, mostly or consistently lie below or above the best fit linear or multi-quadratic regression line in each case. Considering, therefore, Figures 31, 34, 38 and 39, it is clear that no particular fibre type or blend lies consistently above or below the regression lines. From this one can conclude that, in terms of fabric thermal resistance, none of the fibre types of blends behave consistently different to the others, once one allows for differences in the fabric structural parameters, such as mass and/or thickness, the respective points lying scattered around the regression line. These findings are largely in line with those of Gericke and Van der Pol (2010). Other studies, such as by Das and Biswas (2011), Nayak et al. (2009) and Tyagi et al. (2004) in which an effect of fibre type or blend on thermal resistance was observed, may not have taken into consideration possible associated changes in fabric thickness, mass, etc.

Although it can be argued, that a particular fibre, such as wool, may produce a thicker or bulkier fabric due, for example, to its crimpiness, and therefore to better thermal resistance, the counter argument based upon this study, is that by increasing the crimp of another fibre, for example a man-made fibre, a similar result can be obtained. Hence, the difference cannot be attributed to any intrinsic characteristic of the fibre structure per sé.