QUANTIFYING HAIR MOTION 375 generate relatively high combing forces such that the lubricating benefi ts of products can more effectively be demonstrated. This can be attained by using somewhat thicker/denser tresses or, more economically, by chemically damaging the hair. Likewise, looking for shine benefi ts using very straight, heavily pigmented Asian hair would yield minimal sensitivity because of the already highly shiny innate state of the hair. For these reasons, it was considered prudent to look for contributions from the size, shape and nature of hair tresses on motion. In these experiments, longer 25 cm tresses of Asian hair were used that measured 7 g in weight. Instinctively, longer hair might be anticipated to yield more motion—but again, amplitude versus frequency curves suggest a more complex story. Figure 5 shows the effect of tress length on such experiments. Note: all experiments were performed on the same tresses, wherein the length was controlled by the use of a plastic cable tie. That is, the tie could initially be placed around the top of a tress—and then progressively slid downward to yield systematically shorter tress lengths. In general, reducing the tress length leads to amplitude versus frequency curves shifting upward and to the right (higher Amax and fmax). That is, higher amplitudes of motion can be attained but higher frequencies are required to produce this occurrence. Again the shape of these curves illustrates the danger of making conclusions from experiments at a single frequency. For example, from Figure 5, experiments at 1 Hz would suggest pro- gressively higher motion (amplitudes) with increasing hair length, whereas testing the exact same tresses at higher frequencies (≥1.6 Hz) yields the reverse conclusion. Meanwhile, Figure 4. Effect of hair type and treatment on amplitude versus frequency plots.

JOURNAL OF COSMETIC SCIENCE 376 experiments at 1.2 Hz would produce the puzzling conclusion of the longest and shortest tresses giving comparable results, whereas high values result for intermediate lengths. Frequency and energy are directly related (more energy is required to attain higher frequen- cies) and so a means of conceptualizing results in Figure 5 is to suggest that although higher amplitudes can be achieved in shorter tresses, more energy is needed to attain this state. This produces an alternate way for thinking about results in Figure 5. Namely, rather than considering what amplitude results from application of a given frequency—one can eval- uate the frequency (energy) necessary to move the hair at a given amplitude. By means of illustration, Table I shows the frequency necessary to achieve a 40° amplitude of motion in tresses of differing length. It is evident that this amplitude can be obtained via two Table I Frequency Required to Attain a 40° Amplitude of Motion in Hair of Different Lengths Tress length (cm) Frequency to attain 40° amplitude (low side) (Hz) Frequency to attain 40° amplitude (high side) (Hz) 24 0.95 1.25 22 1.02 1.42 20 1.07 1.67 18 1.21 1.92 Frequencies listed in the table are calculated from best fi tting curves (as shown in Figure 5) as obtained using Table Curve 2D® V5.0 by SYSTAT (San Jose, CA). Figure 5. Effect of hair length on the shape of amplitude versus frequency plots.