French’s curve

In the 1820s, another French engineer, Jean Victor Poncelet, working from Borda s theory, designed an undershot vertical wheel with curved blades. Water entered the wheel from below without impact by gently flotving up the curved blades. It then reversed itself, flowed back down the curved blades, and departed the wheel with no velocity relative to the wheel itself. Theoretically the wheel had an efficiency of 100 percent practically, it developed 60 percent to 80 percent, far higher than a traditional undershot wheel. 

Unlike ellipses, parabolas do not lend themselves to simple mechanical drawing aids. The ones occasionally described in texts work crudely. Templates are hard to find. The two best methods for drawing parabolas both involve locating points on the parabola and connecting those points either by eye, or with the help of a draftsman s french curve. 

One of the commonest methods of smoothing a curve is to pin down a flexible lath to points through which the curve is to be drawn and draw the pen along the lath. It is found impossible in practice to use similar laths for all curves. The lath is weakest where the curvature is greatest. The selection and use of the lath is a matter of taste and opinion. The use of French curves is still more arbitrary. Pickering used a bent spring or steel lath held near its ends. Such a lath is shown in statical works to give a line of constant curvature. The line is called an elastic curve (see G. M. Minchin s A Treatise on Statics, Oxford, 2, 204, 1886). 

In the French standard NF C 32-070 (1983), the fire resistance of cables is tested in an oven heated according to a standard curve (cf. Section 3.2.1.2 and Fig. 3.105). In the oven, one or more 700 mm long piece(s) of cable are stretched horizontally at a stress of 2 N/mm. Individual cables are at least 300 mm apart. Each cable core is energized at 0.25 A in a separate circuit through a fuse of 0.5 A and a lamp. When temperature of the oven has reached 900 °C, this level is maintained for 15 min until the end of the test. If none of fuses is ruptured nor any lamp extinguished, the cable is rated CRl, otherwise it is CR2 with respect to its fire resistance. 

The workhorse of the kitchen, the chef s knife is typically between 8 and 12 inches long and falls into two categories German, with a curve at the front allowing for a rocking motion, and French, a straight version that requires an up-and-down slicing motion. 

It can be seen that the dotted curve provides a very good smooth curve representation of the data points. This datafit() function is a computer generated equivalent to the draftsman s French Curve. Although it is not shown in Listing 7.17, the analysis actually generates 6 interpolation points or knots uniformly spaced along the data with a knot at each end of the data range and with 4 internal knots. 

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