Type 301 full hard are also shown in Figure 5). Type 301 full hard is required by MIL-HDBK-5F4 to be  capable of being bent around a rod of diameter six times the thickness of the spring material, without the  occurrence of surface cracking. Using Equation 2, the average bending strain calculated for 0.0254-cm  (10-mil) thick strip bent around a 0.1524-cm (60-mil) diameter rod (neutral surface assumed at the  0.1 778-cm (70-mil) mean diameter) is 14.3 percent, compared to the MIL-HDBKdF requirement for  minimum elongation to failure in simple tension of 8 percent. No similar bending requirement is given for  the extra hard Type 301, as this level of cold work is not controlled by MIL-HDBKd or by ASTM  specifications. Accordingly, it is prudent for the end user to provide specifications for the extra hard  version, rather than rely entirely on the spring vendor’s judgment and practice.  For a limited number of cycles at ambient temperature, strains beyond the yield strength (based on 0.2  percent offset) can be tolerated without failure. From a graph in Votta’s paper, his recommended  allowable stress factor (strain) for less than 5000 cycles is 2.0 percent, for what he calls “safe design”,  using 1095 carbon steel. In the Associated Spring Design Handbook2, a graph is presented showing an  “allowable” (quasi-linear) stress of 2,760 MPa (400,000 psi) for fewer than 260 cycles. In actual practice,  however, the design of constant torque springs is based on empirical data, rather than Votta’s formulas.  In a couple of other major spring manufactures’ design guides, Type 301 is rated at up to 2000 cycles for  strains above 1 .O percent or greater. (Typically 50 to 100 cycles are considered adequate for life testing  of deployables that only operate once in orbit, plus the cycles needed during manufacture and testing).  Normally, one would not be concerned over delayed cracking in typical spacecraft storage environments.  However, for springs stowed at stress levels beyond yield over prolonged periods, this aspect merits  some consideration. Type 301 is on the list of materials considered to be resistant to stress corrosion  cracking; however, when cold reduced to the full hard or extra hard state, a phase transformation from  austenite to martensite occurs, which would logically obviate a totally exempt status. Looking into this  further, the storage atmosphere is typically at controlled humidity, and at the launch site the spacecraft is  usually in an air-conditioned payload housing. One reference, by Phelps and Loginow , cites an  exposure test to atmospheric corrosion at Kure Beach, N.C. of Type 301, 60 percent cold reduced, for  periods of 240 to 370 days, during which the test specimens showed “excellent resistance to stress  corrosion”. However, these specimens were only stressed to 75 percent of the stated yield strength of  1640 MPa (238,000 psi). Data for springs stressed beyond yield, sustained over typical aerospace  storage periods of five years, has not been located. On the other hand, neither has breakage of this type  of spring been reported, due to delayed cracking (or for any other reason) in aerospace usage.  Torque Determination 5  In Votta’s technical paper, he gives a formula for calculating the torque on a constant torque spring motor.  The formula currently derived (Equation 4), based on strain energy, is almost the same as Votta’s except  for the factor in the denominator involving Poisson’s ratio.  (4)  T = Torque  W =Width (Figure 2)  This factor also appears in the quasi-linear stress formula, Eqn. 3, and is conventionally used to adapt the  standard handbook formulas for beam bending of exceptionally wide beams. It results from an elastic  state called “plain strain”, which is applicable to a thin, wide beam (strip) in bending. (An interesting  comment from A. M. Wahl, a noted authority in spring design of that era, was published in the  “Discussion” portion of Votta’s paper. Wahl stated that this factor should have been present in Votta’s  formula. Votta’s response was that their test data showed that this factor did not apply because of energy  lost in transverse [anticlastic] curvature of the straight length of spring between the two spools.)  Equation 4 implies that the torque should be constant with angular displacement. However, as seen from  Figure 3, there is a fairly linear, negative slope to the deployment curve. It is surmised that stresses  beyond yield contribute to the magnitude of the negative slope. Hysteresis is another component of  167