Naval Ordnance and Gunnery
Volume 2: Fire Control
Appendix F — Standard Fire Control Symbols

Appendix F of Naval Ordnance and Gunnery, Volume 2: Fire Control (NavPers 10798-A, 1958) establishes the standard system of fire control symbols approved by the Bureau of Ordnance. These symbols provide a concise notation for the quantities used in surface gunnery, antiaircraft fire control, torpedo, and antisubmarine fire control problems. The system uses capital letters for basic quantities, modified by lowercase letters, numerals, the Greek letter delta (Δ), and the prime mark (′).

The Greek letter delta (Δ) does not render correctly in plain HTML text; it appears in diagrams and formulas as a triangle symbol. Where the original text writes “(triangle)” before a quantity, it means the delta modifier indicating an increment or change in that quantity. The prime modifier (′) indicates a quantity measured in or with respect to the deck plane.

F1. General

Symbols are used in fire control to provide a brief, accurate means of representing quantities which would otherwise require extended definition. The standard system of fire control symbols approved by the Bureau of Ordnance is applicable to the surface and antiaircraft problems and, with certain exceptions, to the torpedo fire control problem and the antisubmarine fire control problem.

Method of forming symbols. The fire control symbols are made up of capital letters, standing for basic quantities, and lower case letters, arabic numerals, the Greek letter delta (Δ), and the prime (′) used as modifying symbols. For example, S_o is made up of a basic symbol S meaning “speed” and a modifying symbol o meaning “of own ship.” Hence, the symbol S_o signifies own ship’s speed.

One basic symbol may be modified simultaneously by a number of modifying symbols, and in certain unusual cases by another basic symbol used as a modifier. Thus, B, bearing, can be modified first to become B_r, relative bearing, then further to cB_r, generated relative bearing, and finally to ΔcB_r, increments of generated relative bearing. Modifiers added ahead of an already modified quantity normally act to modify that quantity further; when additional modifying symbols are added after a basic quantity they may be additive in effect, thus R_j + R_t + R_w + R_m + R_x may be written R_jtwmx.

The prime indicates measurement in the deck plane. B is true bearing measured in the horizontal plane; B′_r (director train) is the same angle measured in the deck plane. B′_r′ (director train, sight not stabilized) adds a second prime indicating the measurement plane is perpendicular to the deck. Similarly, E is elevation measured in a vertical plane and E′ is elevation measured in a plane perpendicular to the deck.

F2. Basic Symbols and Definitions

Symbol	Definition
A	Target angle.
B	Bearing (of target, unless modified), measured in the horizontal plane.
C	Course, measured in the horizontal plane.
D	Lateral deflection (angular measure).
E	Elevation (of target, unless modified), measured in the vertical plane.
F	Fuze setting.
G	Gyro angle (torpedoes).
H	Height of target (normally in feet).
I	Angle of climb or dive (inclination).
K	(Also K1, K2, etc.) Constants.
L	Level angle, measured in the vertical plane.
M	Roll.
N	Pitch.
P	Parallax.
Q	Spread gyro angle (torpedoes).
R	Range.
S	Speed.
T	Time.
U	Average projectile velocity.
V	Elevation prediction (angular measure).
W	Wind.
X	Horizontal deflection component of velocity perpendicular to the vertical plane through the line of sight.
Y	Horizontal range component of velocity in the vertical plane through the line of sight.
Z	Crosslevel angle.

F3. Common Modifying Symbols and Definitions

Symbol	Definition
a	Of torpedo.
b	Of director.
c	Before a quantity: value as generated by the mechanism, as opposed to the observed value. After a quantity: relative to rate control.
d	Before a quantity: time rate of change of that quantity. After a quantity: in or relative to the deck plane or plane perpendicular to the deck.
e	Elevation.
f	Due to standard trajectory.
g	Of gun.
h	Horizontal projection of.
i	Searchlight (illumination).
j	Before a quantity: a correction or partial correction, usually generated by the mechanism. After a quantity: arbitrary correction (spot) to that quantity.
m	Change of initial velocity.
o	Own ship; of or due to.
p	Parallax; of or due to.
q	Relative to the line of sound (ASW term).
r	Relative to own ship.
s	Relative to the line of sight, or in a slant plane.
t	Of or due to target.
u	Of torpedo tube.
v	Vertical projection of.
w	Of or due to wind.
z	Of or due to crosslevel.
Δ	Before a quantity: change in that quantity during a specific time; increment of a quantity.
′	Indicates that a quantity is measured in or with respect to the deck plane.
2	After a quantity: the predicted value for advance position, i.e., at time of flight seconds after firing, or at time of impact or burst.
3	After a quantity: the predicted value for the time of burst of a fuzed projectile, the fuze having been set dead time seconds before firing.

F4. Principal Fire Control Quantities

A

Target angle. The angle between a vertical plane through the direction of target motion and the vertical plane through line of sight, measured in the horizontal plane clockwise from the direction of target motion.

B

True target bearing. The angle between a north-and-south vertical plane and the vertical plane through the line of sight, measured in a horizontal plane clockwise from the north.

B′_gr

Gun train order. The ordered angle between the fore-and-aft axis of own ship and a plane through the gun axis perpendicular to the deck plane, measured in the deck plane clockwise from the bow of own ship, without parallax correction.

B_r

Relative target bearing. The angle between the vertical plane through the fore-and-aft axis of own ship and the vertical plane through the line of sight, measured in a horizontal plane clockwise from the bow of own ship.

B′_r

Director train (stabilized sight). The angle between the vertical plane through fore-and-aft axis of own ship and the vertical plane through the line of sight, measured in the deck plane clockwise from the bow of own ship.

B′_r′

Director train (sight not stabilized). The angle between the fore-and-aft axis of own ship and the plane through the line of sight perpendicular to the deck plane, measured in the deck plane clockwise from the bow of own ship.

B_w

True direction of true wind. The angle between north and the direction from which the true wind is blowing, measured in a horizontal plane clockwise from north.

B_wg

Predicted wind angle. The angle between the direction from which the wind is blowing and the vertical plane through the line of fire, measured in the horizontal plane clockwise from the direction from which the wind is blowing.

B_ws

Wind angle. The angle between the direction from which the wind is blowing and the vertical plane through the line of sight, measured in the horizontal plane clockwise from the direction from which the wind is blowing.

C_o

Own-ship course. The angle between the north-and-south vertical plane and the vertical plane through the fore-and-aft axis of own ship, measured in a horizontal plane clockwise from north.

C_t

Target course. The angle between the north-and-south vertical plane and the vertical plane through the direction of motion of the target, measured in a horizontal plane clockwise from north.

C_w

B_w − 180°. The angle between north and the direction toward which the true wind is blowing, measured in a horizontal plane clockwise from north.

C_ws

Wind angle. The angle between the direction toward which the wind is blowing and the vertical plane through the line of sight away from own ship, measured clockwise in a horizontal plane.

cB

Generated true target bearing. (See definition of B.)

ΔcB

Increments of generated true target bearing.

cB_r

Generated relative target bearing. (See B_r.)

ΔcB_r

Increments of generated relative target bearing.

cB′_r

Generated director train (stabilized sight). (See B′_r.)

ΔcB′_r

Increments of generated director train (stabilized sight).

cB′_r′

Generated director train (sight not stabilized). (See B′_r′.)

ΔcB′_r′

Increments of generated director train (bearing correction).

cE

Generated target elevation. (See E.)

ΔcE

Increments of generated target elevation.

ΔcE_b

Increments of generated director elevation. ΔcE_b = ΔcE + L.

cR

Generated present range.

ΔcR

Increments of generated present range.

D_d

Deck deflection (stabilized sight). The angle representing total deflection in the deck plane; it is added to director train to obtain gun train order, B′_gr. D_d + B′_r = B′_gr and D_d = jD_d + D_z.

D_d′

Deck deflection (sight not stabilized). Angle representing total deflection in deck plane; it is added to director train to obtain gun train order, B′_gr. D_d′ = D_s + D_z.

D_f

Drift correction. Deflection to compensate for drift of projectile, measured in the horizontal plane.

D_fs

Drift correction. The lateral deflection angle to compensate for drift of a projectile, measured in the slant plane through the predicted target position.

D_j

Deflection spot.

D_s

Sight deflection. Computed angle between vertical plane through line of sight and vertical plane through gun axis (neglecting parallax), measured in the horizontal or slant plane depending on system used.

D_t

Relative motion deflection prediction. Deflection prediction to compensate for relative motion of own ship and target during time of flight.

D_w

Wind deflection prediction. Deflection prediction to compensate for the effect of apparent wind on the projectile.

D_z

Trunnion tilt train correction. Approximate correction in gun train order to compensate for tilting of gun trunnions in crosslevel.

dB_r

Angular bearing rate. In the horizontal plane. The time rate of change of relative target bearing.

dB_s

Angular bearing rate in slant plane. The time rate of change of target bearing measured in the slant plane through the line of sight.

dE

Angular elevation rate. The time rate of change of target elevation.

dH

Rate of climb. The time rate of change of target height.

dR

Range rate. The time rate of change of range.

dR_h

Horizontal range rate. The time rate of change of horizontal range.

dR_m

Alteration to prediction range rate to compensate for changes in I.V.

dR_s

Prediction range rate. Direct range rate corrected for the effect of deflection and elevation rates, and for changes in I.V.

dR_xe

Range rate correction. Correction to prediction range rate for the effect of the deflection and elevation rates.

E

Target elevation (stabilized sight). The angle between the horizontal plane and the line of sight, measured in the vertical plane through the line of sight. E = E_b − L.

E′

Target elevation (sight not stabilized). The elevation above the horizontal of the line of sight, measured in the plane perpendicular to the deck, through the line of sight.

E_b

Director elevation (stabilized sight). The elevation of the director line of sight above the deck, measured in the vertical plane through the line of sight.

E′_b

Director elevation (sight not stabilized). The elevation of the director line of sight above the deck, measured in a plane perpendicular to the deck, through the line of sight.

E_g

Vertical gun elevation. The elevation of the gun above the horizontal, measured in a vertical plane through the gun axis.

E′_g

Gun elevation order. Ordered elevation of the gun above the deck plane, measured in a plane through the gun axis perpendicular to the deck plane.

E₂

Predicted target elevation.

F

Fuze setting order. Fuze setting in seconds.

H

Target height. Vertical distance between the target and the horizontal plane through the director sights.

jB

Initial or corrective setting to generated target bearing.

jB_c

Linear deflection rate correction. Rate control correction affecting linear deflection rate.

jB′_r

Correction to director train for effect of deck tilt. (Refers director train to the horizontal plane, sight stabilized.)

jB′_r′

Correction to director train for effect of deck tilt. (Refers director train to the horizontal plane, sight not stabilized.)

jD_d

Partial deck deflection. An intermediate value used in computing D_d.

jE

Initial or corrective setting of generated target elevation.

jE_c

Linear elevation rate correction. Rate control correction primarily affecting linear elevation rate.

jdR

Direct range rate correction. The rate control correction primarily affecting range rate.

jdR_h

Horizontal range rate correction. Rate control correction primarily affecting horizontal range rate.

jH_c

Rate-of-climb correction. Rate control correction primarily affecting rate of climb.

jR

Initial or corrective setting of generated range.

jR_c

Linear range correction. Applied to generated range.

jR_m

Partial range prediction to compensate for changes of initial velocity.

jR_x

Partial range prediction to compensate for deflection exclusive of drift.

jV_s

Partial sight angle. (Cam output.)

L

Level angle. The angle between the horizontal plane and the deck plane, measured in the vertical plane through the line of sight about an axis in the horizontal plane. (Positive when the deck toward the target is below the horizontal plane.)

L′

Level angle. The angle between the horizontal plane and the deck plane measured in the plane perpendicular to the deck through the line of sight about an axis in the deck. (Positive when the deck toward the target is below the horizontal plane.)

L_j

Selected level angle. Any arbitrary selected value of level (for those systems in which the directors measure level as L).

L′_j

Selected level angle. Any arbitrary selected value of level (for those systems in which the directors measure level as L′).

M

Roll. The instantaneous value of the angle between the reference plane and the horizontal, measured in an athwartship vertical plane.

N

Pitch. The instantaneous value of the angle between the reference plane and the horizontal, measured in a fore-and-aft vertical plane.

P_e

Elevation parallax correction for vertical base. (In main-battery systems P_v is used for this quantity.)

P_h

Train parallax correction for horizontal base.

P_v

Elevation parallax correction for horizontal base. (See note on P_e above.)

R

Observed present range.

RdB_s

Linear deflection (bearing) rate. The horizontal component of relative motion between target and own ship, at right angles to the vertical plane through the line of sight.

RdE

Linear elevation rate. The component of relative motion between target and own ship, at right angles to the line of sight and in the vertical plane through the line of sight.

R_h

Horizontal range. The projection of the range on a horizontal plane.

R_j

Range spot.

R_m

Range prediction to compensate for changes in I.V.

R_t

Range prediction to compensate for relative motion of own ship and target.

R_tg

Correction in fuze range for dead time.

R_w

Range prediction to compensate for effect of apparent wind on projectile.

R_x

Range prediction to compensate for deflection exclusive of drift.

R₂

Advance range (or predicted range).

R₃

Fuze range. R₂ − R_tg.

S

Target speed. (For an air target, this represents speed along a line of flight with respect to the earth.)

S_h

Target horizontal ground speed. The horizontal component of air target speed with respect to the earth.

S_o

Own-ship speed. The speed of own ship relative to the earth.

S_s

Diving speed of target. Speed along the line of sight, or direct range rate.

S_w

True wind speed. The horizontal velocity of wind with respect to the earth.

T

Time. Generated by the regulated time motor.

T_f

Time of flight.

T_g

Dead time. Time in seconds between the setting of the fuze and the firing of the projectile.

V

Total elevation prediction. The approximate amount that target elevation changes during the time of flight. V = V_tw − V_x + V_j.

V_f

Superelevation. The angle the gun must be elevated above the predicted line of sight to compensate for the curvature of trajectory in the vertical plane.

V_fm

Correction to superelevation for a change in I.V.

V_j

Elevation spot.

V_s

Sight angle. The angle, computed in a vertical plane, which the gun must be elevated above the line of sight or the horizontal (depending on the system) in order to hit the target when the deck is horizontal.

V_t

Relative motion elevation prediction. Compensates for the relative motion of own ship and target during the time of flight.

V_w

Wind elevation prediction. Compensates for the effect of apparent wind on the projectile.

V_x

Complementary error correction. Correction to elevation prediction to compensate for deflection prediction.

V_z

Trunnion tilt elevation correction. Correction to gun elevation to compensate for the effect of crosslevel.

W_rD

Deflection wind rate. The component of apparent wind velocity affecting deflection prediction.

W_rE

Elevation wind rate. The component of apparent wind velocity affecting elevation prediction.

W_rR

Range wind rate. The component of apparent wind velocity affecting range prediction.

X_o

Horizontal component of own-ship velocity at right angles to the vertical plane through the line of sight. (Deflection component.)

X_t

Horizontal component of target velocity at right angles to the vertical plane through the line of sight. (Deflection component.)

X_w

Component of true wind velocity across line of sight.

X_wg

Horizontal component of true wind velocity, at right angles to the vertical plane through the line of fire. (Deflection component.)

X_wgr

Horizontal component of apparent wind velocity, across the vertical plane through the line of fire. (Deflection component.)

X_wr

Component of apparent wind velocity across line of sight.

Y_o

Horizontal component of own-ship velocity in the vertical plane through the line of sight. (Horizontal range component.)

Y_t

Horizontal component of target velocity in the vertical plane through the line of sight. (Horizontal range component.)

Y_w

Component of true wind velocity along line of sight.

Y_wg

Horizontal component of true wind velocity, in the vertical plane through the line of fire. (Horizontal range component.)

Y_wgr

Horizontal component of apparent wind velocity, in the vertical plane through the line of fire. (Horizontal range component.)

Y_wr

Component of apparent wind velocity along line of sight.

Z_d

Crosslevel angle measured about an axis in the deck; the angle, measured about the intersection of the plane of the deck with the vertical plane through the line of sight, between the vertical plane and a plane perpendicular to the deck through this axis. (Positive if when you face the target the right-hand side of the ship is up.)

Z_dj

Selected crosslevel angle. Any arbitrary value of crosslevel when crosslevel is measured as Z_d.

Z_h

Crosslevel angle measured about an axis in the horizontal; the angle, measured about the intersection of the horizontal plane with the vertical plane through the line of sight, between the vertical plane and a plane perpendicular to the deck through this axis. (Positive if when you face the target the right-hand side of the ship is up.)

Z_hj

Selected crosslevel angle. Any arbitrary value of crosslevel when crosslevel is measured as Z_h.