RN Subs

Appendix B

Calculations of power and speed

(See Appendix D Item 5, regarding reference source speed/power data anomalies)

The data from the USN purchase specifications for the SARGO 1, SARGO ll and GUPPY 1 cells is available and forms the basis of these calculations using the simple formulae - Power equals Volts X Amps = Watts and 746 watts = one horse power. The performance of the electric motors is known from the surface data.

The electric power input to submarine motors is greater than the mechanical power output to the shaft due to internal losses, giving an efficiency figure in the order of 90%. This figure can vary from 92% down to 88% dependent on motoring conditions and a sensible choice is made for each calculation.

It should be noted that for a given submarine DC propulsion motor - speed is proportional to the armature supply voltage ; it can then be increased further by lowering the field current, this increases the armature current.

The Fleet Submarine

Alden and others report that the SARGO I cells in the unconverted Fleet Submarine, gave 9 knots maximum submerged, endurance of one hour, propulsion power 2400 shp

Navpers 16162. - "For submerged operation, using various combinations of armatures and taking power from the batteries, the motors developed power ranging from 30 hp to 1719 hp per propeller shaft and give a speed range from 38 rpm to 219 rpm"

The figure of 1719 hp per propeller shaft submerged (total 3438 shp) is higher than the 2400 shp given by other sources. The anomaly is further pursued in Appendix D. Item 3.

The two main battery groups, one forward and one aft, each consisted of 126 individual SARGO I cells connected in series. (Fig 4).

The two batteries connected in parallel to give an average voltage over the hour of 204 v at a discharge current of 5320 x 2 total amps 10,640. Some of this current would be needed for auxiliary supplies, as mentioned below.

A simple example calculation -

(10,640 amps x 204 volts X 0.92 eff)/746 hp = 2677 shp.

From this figure might need to be deducted the auxiliary load -

200 volts x 500 amps =134 hp.

So -

2677 - 134 = 2543 shp.

Reasonably close to the figure stated by Alden. The figure of 134 shp will used in all the following calculations, it also allows for the main motor field currents as high as 60 amps at 200 volts. It is at its highest value when the slowest speed is required at any given voltage suppled to the armatures.

Obviously the 300 kw (400 hp) auxiliary diesel - generator could not be used when submerged. This was removed in GUPPY submarines.

GII

The two main battery groups, one forward and one aft, each consisted of two batteries each of 126 individual GUPPY 1 cells connected in series that were permanently connected in parallel forming a single battery.504 cells in total. (Fig 4) Thus the cell Ampere Hours and amps are times 2 in the calculations.

Half hour rate

The specified maximum battery current at the half hour rate with batteries in Series for maximum speed submerged was (2 x 6775 amps) = 13550 amps (Average volts 390).

Calculate the maximum propulsion power -

(13550 x 390 x 0.88) / 746 = 6,234 shp.

Deduct 134 hp for auxiliary loads and 6100 shp becomes a realistic power to the shafts, with an acceptable 13% motor overload for 30 minutes

One hour rate

The specified maximum battery current at the one hour rate with batteries in Series for maximum speed submerged at this rate was (2 x 4340 amps) = 8680 amps (Average volts 424)

Calculate propulsion power, but for one hour -

(8680 x 424 x 0.9) / 746 = 4440 shp.

Deduct 134 hp as the auxiliary load and 4306 shp power to the shafts

Speed

Alden reports submerged speeds of 18.2 knots for the two GI boats and 16 knots for the fully operational GII boats

So we have a stated speed rating of 16 knots for the GII at a calculated 1/2 hour discharge rate and power of 6100 shp then speed at the one hour rate can be calculated from the already calculated power of 4306 shp.

6100 / 4306 = 1.4166, cube root = 1.123. 16 / 1.123 = 14.25 knots.

GIA/GIIA

The two main battery groups, one forward and one aft, each consisted of 126 individual SARGO II cells connected in series. (Fig 4)

Half hour rate

The specified maximum battery current at the half hour rate with batteries in Series for maximum speed submerged was 10,200 amps, average volts 364.

Calculated power -

(10,200 x 364 X 0.90) / 746 = 4479 shp.

Deduct the 134 hp for auxiliary load and we have 4345 shp to the shafts.

One hour rate

The specified maximum battery current at the one hour rate with batteries in Series for maximum speed submerged was 10,200 amps, average volts 404.

Calculated power -

(6,800 x 408 X 0.90) / 746 = 3347 shp.

Deduct the 134 hp for auxiliary load and we have 3213 shp to the shafts.

Speed

As Alden's figures for the GIA/GIIA are ambiguous (see note), giving something between 14 and 15, then initially we will take the GIA/GIIA as both being rated at 14.5 knots.

So we have a stated speed rating of 14.5 knots for the GIA/GIIA at a calculated 1/2 hour discharge rate and power of 4345 shp then speed at the one hour rate can be calculated from the already calculated half hour rate power of 4345 shp.

4345 / 3213 = 1.352 - cube root = 1.106. 14.5 / 1.126 = 13.1 knots.

Footnote

The propulsion power of the GII at the one hour rate is 4306 shp with a motor current of 8680 - 500 and voltage of 424.

The propulsion power of the GIA/GIIA at the half hour rate is 4345 shp with a motor current of 10.200 - 500 and voltage 364.

The motor efficiency for the two currents would be different giving slightly changed the results, although the same motors are used in each case at about the same power.

Another method of calculation

Recent opportunity to read Friedman's book "SUBMARINE DESIGN AND DEVELOPMENT " P.65, gave an interesting new figure.

He states, Quote "At periscope depth on batteries, over the 8-10 knot range, an unstreamlined Fleet Submarine required 2.25 times as much power as a 'GUPPY'. Unquote.

This is an interesting figure that enables a calculation of maximum shaft power not reliant on the cell specification - it seems likely to have come from an official trial source. The periscope depth is a minor complication as slower speeds tend to be achieved than at 90 feet, but still useful to see if all the figures stay within the limits of the GUPPY power/speed envelope derived from the battery specifications.

Taking Alden's propulsion figures for the unconverted Fleet submarine of 9 knots at 2400 shp, the 2400/ 2.25 = 1067 shp gives the power of the GUPPY II at 9 knots.

16/9 gives 1.777, cubed to obtain required power increase = 5.6 x 1067 = 5995 shp for 16 knots. Very similar to the earlier 6,100 shp calculated in the G1 and GII section using the GUPPY 1 cell specification, allowing for the margin of error using stated speeds and estimated efficiency figures

For the GIA/GIIA, at a maximum of 14.5 knots - 14.5/9 gives 1.GII,cubed = 4.18 = 4.18 x 1067 = 4462 shp for 14.5 knots.

4462 shp is acceptable compared with the earlier figure of 4345 shp calculated from the SARGO half hour battery data, when merely changing the estimated efficiency figure from 90% to 92% will produce 4445 shp instead of 4345 shp. See earlier footnote.

CONCLUSION

From the above calculations, a good idea has been gained of the submerged speeds achieved by the two basic GUPPY conversions.

GIA/GIIA - 14.5 knots at the half hour battery discharge rate, propulsion power 4345 shp
GIA/GIIA - 13.1 knots at the one hour battery discharge rate, propulsion power 3213 shp
GII -16.0 knots at the half hour battery discharge rate, propulsion power 6100 shp
GII -14.25 knots at the one hour battery discharge rate, propulsion power 4306 shp

SLOW SPEED ENDURANCE EXAMPLE

The speed trials of HMS TACITURN suggest the 20 hour battery discharge figures would be a useful point to start

Each 126 cell battery is in parallel with the other(s). Four in GII and two in GIA/GIIA.

Assume the Hotel load was a constant 200 amps in each submarine, similar motor efficiency (0.92) and drag resistance.

SARGO II cell capacity ampere-hours at the 20 hour rate was (11800 x 2) 23,600, with a discharge of (590 x 2) 1180 amps, average volts 244, final volts 215. (2 - 126 cell batteries) GIA/GIIA submarine.

1180 - 200 = 980. then (980 x 244 X 0.92) / 746 = 295 shp. Taking the already calculated power 4345 shp at 14.5 knots - speed at 295 shp = 4345 / 295 = 14.73. cube root = 2.45. 14.5 knots / 2.45 = 5.9 knots.

20 hours by 5.9 knots = 118 miles endurance at 5.9 knots.

GUPPY 1 cell capacity ampere-hours at the 20 hour rate was (7400 x 4) 29,600,

Divide the GUPPY 1 cell 20 hour AH by the SARGO II 20 hour amps - 29,600 / 1180 = 25 hours. 5.9 knots x 25 hours = 147.5 miles endurance at 5.9 knots.

Note The 25 hour rate (If specification data was available) no doubt has a larger figure of ampere hours than the 20 rate, this would modestly extend the endurance.

Appendix C

Engine and motor detail

The main diesel generator sets and propulsion motors of the similar WWII Fleet Submarine of the GATO, BALAO and TENCH classes.

1. General Motors V-16 type. There were two engine designs in this category, the 16-278A and 16-248. Each engine had two banks of 8 cylinders, each arranged in a V-design with 40 degrees between banks. Each engine was rated at 1600 BHP at 750 rpm. Both engines were equipped with mechanical or solid type injection and had a inflow valve and port system of scavenging. 2 cycle.. Main Propulsion Dieselise, NAVPERS 16161

OR

2. Fairbanks-Morse opposed piston type, Model 38D 8 1/8. This model number included two engines, one a 10-cylinder and the other a 9-cylinder engine, 2 cycle.. Both engines were rated at 1600 bhp at 720 rpm. Main Propulsion Diesels, Navpers 16161

The rating of these engines was apparently modified to suit snorkelling. This reduced the surface rating from 5400 shp to 4610 shp. Alden reports 4610 shp for all snorkel submarines but only specifically says for the Loon SSG conversion, "Rated 4160 shp surfaced after installation of snorkel" - max surface speed 17/18 knots" See anecdote Appendix E.

The Main generators were rated at approximately 2650 amperes at 415 volts and 1100 kilowatts. Submarine Electrical Installations, Navpers 16162. That is a total of 10,600 amps at 415 volts.

Main motors used in a gear drive installation were classed as high-speed motors and each was rated for continuous duty at approximately 1370 hp, 415 volts, 2600 amperes, and 1300 rpm.On the latest classes of submarines main motors and reduction gears have been replaced by two 2700-hp double armature motors, directly connected to propeller shafts, one to the starboard and on to the port shaft. Submarine Electrical Installations, Navpers 16162

4 x 1100 kW = 4400 kW electrical output from generators to the motors - .5400 shp x 746 = 4028 kW motor output to shafts

Therefore efficiency of the motors is 4028/4400 = 91.6%. The efficiency would have dropped when the motors were overloaded as in GII.

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