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By using the speed brake do we reduce the speed or do we increase the descent rate or does both happen simultaneously? Could someone please explain the concept

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The two most common types of speed brakes are fuselage mounted and top of the wing mounted speed brakes.

The effect of both types is the increase of drag. Top of the wing mounted speed brakes also decrease lift.

The "end result" of using speed brakes is actually up to the pilot to decide.

First use case would be the "both" scenario: most efficient approach profile considering fuel consumption would be to simply idle glide from cruising altitude all the way to the final approach fix. Unfortunately traffic situations and geographical features do not always permit this, and therefore trajectory management may be necessary: the plane might need to descent at faster rate than would be possible for a given airspeed restriction. In this case the pilot would choose to use the speed brake to achieve both the steeper descent rate and airspeed.

Second use case would be simple speed management: modern passenger planes are quite "slippery": they can be hard to slow down. in these cases it might be necessary to use speed brakes to bleed off the airspeed to match the traffic flow and approach procedures of the airport. In this case, the speed brake are applied to slow down while maintaining "normal" descent rate or even level trajectory.

Top of wing mounted speed brakes / spoilers require some trim adjustment to maintain the trajectory of the plane. The speed brake itself may or may not induce this trim change. Fuselage mounted ones such as on BAe-146 are pretty much trim neutral.

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Every implementation of a speed-brake that I've come across is basically a method of increasing drag, rather like putting your foot on the ground with a scooter, and slightly differently from most wheeled vehicles, which only brake indirectly.

Secondary effects on the aircraft are exactly that - 'secondary' - and entirely dependant both on what the aircraft is doing, and what controls are in play. For example, if the aircraft has auto-throttle, and the speed brake is somehow deployed without the management system being aware, then the throttles will be advanced until the aircraft regains the selected airspeed.

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The practical answer is they increase angle of descent.

How they do it is a bit more complicated. Aircraft in level flight at constant speed have the all familiar 4 forces of flight: thrust and drag, lift and gravity, in balance.

The speed brake creates more drag, slowing the aircraft, which reduces lift. The aircraft, if it is staticly stable, will pitch down until thrust + gravity component (sine angle of descent × weight) = drag

Since lift is proportional to velocity squared, aircraft pitch (to the horizon) will be very sensitive to a reduction in airspeed.

If the aircraft is not staticly stable (most are), then the reduction of speed will be more noticable.

Another case to consider is that the speed brake, such as a flap, can increase the coefficient of lift (of the wing). In this case, the aircraft will have both a decrease in airspeed and an increase in angle of descent.

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