fully computerized bombsights were introduced, which combined the bombing with long-range navigation and mapping. Modern aircraft do not have a bombsight but use highly computerized systems that combine bombing, gunnery, missile fire and navigation into a single head-up display. The systems have the performance to calculate the bomb trajectory in real time, as the aircraft manoeuvres, and add the ability to adjust for weather, relative altitude, relative speeds for moving targets and climb or dive angle. That makes them useful both for level bombing, as in earlier generations, and tactical missions, which used to bomb by eye. Theory Forces on a bomb The drag on a bomb for a given air density and angle of attack is proportional to the relative air speed squared. If the vertical component of the velocity is denoted by and the horizontal component by then the speed is and the vertical and horizontal components of the drag are: where is the coefficient of drag, is the cross-sectional area, and is the air density. These equations show that horizontal velocity increases vertical drag and vertical velocity increases horizontal drag. These effects are ignored in the following discussion. To start with, consider only the vertical motion of a bomb. In this direction, the bomb will be subject to two primary forces, gravity and drag, the first constant, and the second varying with the square of velocity. For an aircraft flying straight and level, the initial vertical velocity of the bomb will be zero, which means it will also have zero vertical drag. Gravity will accelerate the bomb downwards, and as its velocity increases so does the drag force. At some point (as speed and air density increase), the force of drag will become equal to the force of gravity, and the bomb will reach terminal velocity. As the air drag varies with air density, and thus altitude, the terminal velocity will decrease as the bomb falls. Generally, the bomb will slow as it reaches lower altitudes where the air is denser, but the relationship is complex. Now consider the horizontal motion. At the instant it leaves the shackles, the bomb carries the forward speed of the aircraft with it. This momentum is countered solely by drag, which starts to slow the forward motion. As the forward motion slows, the drag force drops and this deceleration diminishes. The forward speed is never reduced entirely to zero. If the