Gunni has it right on. With the board up or partly up, the boat in the worst conditions that lead to broaching will allow the boat to 'skid' sideways rather than 'tripping over' the CB in the full down position, or 'tripping over the keel' on a fixed keel boat.
However !!!! if the boat is now skidding sideways, the effective water line length though the section of the hull in the direction of 'travel' (typically across the beam!) becomes the 'new' waterline length essentially based on the 'beam' dimension and the so-called hull speed goes down (by approx. one third) and the boat can radically heel over to leeward, then recover and if the wave formation is 'correct' at this instant the boat then can "broach to windward" because of the radical formed 'bow wave' due to the vastly reduced waterline length from the 'skid'!!!!!
With a CB boat with board up, etc. when one feels a broach coming through the increasing helm pressure 'warning' ... do anything possible to bear-OFF straight down wind and 'hold on' while attempting to keep the boat 'directly UNDER' the mast, in such blammo conditions if you dont keep the boat 'under' the mast (including when 'pitching') you increase the risk of broaching.
The effect of the mainsail when going downwind is that of a 'lever', a lever that can be at up to 90° to the boats centerline and which tends to turn the boat because of its 'lever arm'. Reefing also reduces the 'lever arm' as well as 'depowers' the force of the lever as well as the forward speed. Dousing the main reduces the 'lever arm' to 'nil'.
Having just a small jib only with main doused to hold the bow 'somewhat' downwind is good practice. However once you go much above 'hull speed' and the boat is radically 'plunging and burying' into wave faces and momentarily stopping while the small jib is still 'driving hard', still can lead to a broach (or a pitch pole) ... at these times its better to 'head up' ontp a more broad reach, call it quits and heave-to; or, simply 'run' with bare poles.
In broaching, the boat is typically attempting to go faster than its so-called hull speed and is creating a 'great resistance' on the hull in doing so ... and the action of the sails, principally the mainsail's 'lever arm' in reaction to the wind forces attempts to get the sails/mast, etc. into a more 'equilbrium stable' attitude: .........the sails/mast, etc. downwind and 'in front' of the boat, and the 'lever arm' by turning the boat into a 'broach', a pitch-pole (broaching through the vertical plane), ..... or into a 'submarine'.
Know your 'hull speed' and try not exceed it when in blammo conditions, ..... unless you can keep a boat 'planing' without 'death wobbling'. The problem with 'planing' is if the conditions get 'worse', you will have to 'turn through' the wind to heave-to, or douse, etc. and thats when you can get into 'real trouble' as well as 'shredding the jib', etc. Not exceeding much above hull speed is good practice for 'safety' on just about any sailboat when in 'tough' conditions.
