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While the upper section provides more general information, this will provide more specifics to get an a more optimal amount value of bolt torque.

Max Tensile Load

First we must calculate the maximum tensile load of the bolts being used. This is the measurement of the maximum amount of tension force the bolt can withstand before it fractures.  In the case of Hermes 3, we are using 5/16-18 by 5/8" Grade 8 Steel Bolts. 

The equation for this is:

P = St x As

P = maximum tensile load or clamp load (lbs,. N)

St = tensile strength (psi, MPA)

As = tensile stress area (sq. in, sq. mm)

Using the following spreadsheet, we find that the tensile stress area of our Bolts in inches squared is 0.052. The tensile strength of our material (which in this case is Grade 8 Steel), is approximately 150000 lbs/in^2.

From this we can calculate our maximum tensile load:

P = 0.052 x 150000 == 7800 lbs 

This is the maximum load, however we cannot use this value for calculating our torque specification, because a factor of safety is necessary.  The standard for this is around 75% of the calculated maximum tensile load.  When a safety factor is added, the new value is:

F (optimal clamp load) = 0.75 x 7800 == 5850 lbs

K Value, or the Nut Factor

In the equation for calculating torque, which is T = K x d x F, the value K is the most variable of the values.  While d (the nominal diameter) and F (the clamp force) have very simple calculations to acquire their values, K is much more complex. 

In simple terms, K can be thought of as a measurement of anything that increases or decreases friction between the threads of the nut. A more in depth description of K and its factors can be found in this guide on fasteners. In this wiki page, we will just provide more basic estimations of the K value needed.

The bolts we are using are non-plated black finish, so the K value we will use for this calculation of the torque will be 0.20

Side Note: One reason we do not used zinc-plated bolts is because zinc becomes a gas at 300 degrees C, and our rocket burns at around 2800 degrees C. 

Torque Calculation

Now that we have our tensile load value, as well as our K factor value, the optimal torque can be calculated. 

The equation for torque, as mentioned previously, is:

T = K x d x F

K = Nut Factor

d = nominal diameter of the bolt (in,. mm)

F = tensile load (lbs., N)

For our bolts the diameter is 5/16 of an inch, or 0.3125 inches. So our calculation is:

T = 0.2 x 0.3125 x 5850 == 365.625 in/lbs

365.625/12 == 30.5 ft/lbs

30.5 ft/lbs is now our final value for the optimal torque. This is necessary to guarantee that the bolt is not too loose (which would cause our seal to not be as strong), or too tight (which would deform our bolts and potentially damage the material being clamped).