Introduction
One sees in many places maximum speeds quoted for various torpedoes. My concern here is primarily with the Wikipedia article [3] on the Spearfish torpedo, or rather with the article's sources for the quoted speed of 80kts. It should also be noted that other sources, which I no longer have access to, IIRC claim SF was tracked at AUTEC (Atlantic Undersea Test and Evaluation Center, Andros Island, Bahamas) at 90kts (Friedman's book on weapon systems 1992 [1]. I will say something about this later.).
A rule of thumb often applied when designing homing torpedoes is that the maximum speed should be ~1.5 times the maximum speed of the target.
Derivation of the Energy Optimality of 3/2 Rule for a Tailchase
Notation: Weapon speed \(v_w\), target speed \(v_t\), initial range \(d_0\).
Assumptions: The drag on the weapon goes as \(v_w^2\) (high Reynolds number, and also assuming changing weapon incidence with speed does not bugger this dependence up too much), the weapon is faster than the target (\(v_w>v_t\) )
\[\text{Drag}=kv_w^2\]\[\text{Power}=kv_w^3\]\[\text{Time to Intercept}=\frac{d_0}{v_w-v_t}\]
\[\text{Distance to Intercept for Tail Chase}=\frac{d_0v_w}{v_w-v_t}\]
\[\text{Energy to Intercept}=E=\frac{kd_0v_w^3}{v_w-v_t}=\frac{Kv_w^3}{v_w-v_t}\]
The speed for a minimum energy for tail chase intercept is found when \(\frac{dE}{dv_w}=0\):
\[\frac{dE}{dv_w}=\frac{3Kv_w^2}{v_w-v_t}-\frac{Kv_w^3}{(v_w-v_t)^2}=0\]
Which after rearrangement gives \(v_w=\frac{3}{2}v_t\).
Now when SF was designed the bogyman was the Soviet Project 705 (Alpha) class submarine, which had a maximum speed variously reported from 40 to 45kts. In which case one would expect the maximum speed of SF to be based on this (if achivable) and be ~60 to 67.5kts. As an aside the only reliable information in the open press seems to be an item in the NYT [2] quoting the claimed underwater speed report for the NST7525 Engineering Test Vehicle (ETV) of 80mph (70kts). At the time though it was reported in a number of places, presumably sourced from a Marconi press release. The figure we normally saw in the technical press was for 70kts, which somebody presumably converted and rounded to 80mph for the "popular" press. A plausible explanation for the claimed 80kt speed for SF may be the confusion between mph and kts, the NYT report being 80mph.
Disinformation of AUTEC Tracking Quote
Now the claim that SF was tracked at 90kts [1] can be dismissed as disinformation. When tracking a source the source speed estimate has an error, which can be large when there is little tracking history but should reduce as the history builds up. So it is entirely possible that a source could, initially, be "tracked" at a speed very different from its actual speed, and if this is remarkable enough for it to be reported.
We can also do a plausibility check on such a speed. Suppose that the power source of a torpedo can produce the power to drive the weapon at such a speed. Also suppose that the propulsive range of the weapon at say ~30kts is ~50km (which seem to be typical-ish firgures one sees for torpedo low speed and range). Then as the energy required to go a fixed distance goes as \(v^3\) the propulsive endurance will fall to <2km at 90kts (assuming no loss of efficiency in the propulsion system, and no endurance used up prior to going to 90kts at a lower speed). If however the low speed were 24kts for a range of 50km, then the range at 90kts is <1km, and at 70kts is ~2km. How useful these ranges would be, at these speeds, I don't know.
( I no longer have access to [1] as I left my copy behind when I retired from BAE. If my memory is playing me false this could have been 80kts rather than 90, in which case it could be the source of the Wikipedia references claims?)
Speed Requirements for Anti-Torpedo Torpedoes
One might expect the above argument to also hold for ATTs, but it does not. If you are an ATT the last thing you want is to end up in a tail chase, you never want to be chasing a homing weapon back towards a friendly ship, among other reasons.
The constraints on an ATT engagement mean that the ATT needs to be in a near head-on geometry when it starts its search and homing. To home stably from such a geometry requires that the ATT at least equal the speed of the target (or if you can ensure that the target is dead ahead of the ATT at acquisition then any speed will suffice for the ATT). A speed advantage over the target is highly desirable as it makes homing more robust, but if the target is capable of 60kts+ one is already near practical sonar and propulsion limits. In such a case 90kts would be desirable but would be difficult engineering and costly, which has not stopped us in the past from at least studying the practicality of very high speed ATTs.
That it is desirable for an ATT to at least match the speed of its target suggests that high speed may be part of a torpedoes counter measure suite to ATTs.
References
1. Friedman, Norman, The Naval Institute Guide to World Naval Weapon Systems, 1992 edition.
2. A U.S.-British Torpedo Fight, New York Times, May 14th 1981.
3. Wikipedia contributors, Spearfish torpedo, Wikipedia,The Free Encyclopedia https://en.wikipedia.org/wiki/Spearfish_torpedo ,retrieved 2021-09-09.
