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./heron --use examples/aviation/C172-Takeoff.tesl
This specification illustrates the TESL language with a simple takeoff scenario. It depicts the computation of quantities and units for time, speed and altitude. Performance speeds (IAS) of a light aircraft such as Cessna 172 are given as:
- VR = 55 kt
- Vertical speed in climb: 1200 ft/min
The TESL language allows to define arithmetic relations between clock timeframes. These are called tag relations and allow to describe unit conversions:
// Unit conversion between [s] and [min]
tag relation time-S = 60. * time-MIN
// ... and between [kt] and [m.s^-1]
tag relation speed-KT = <3600/1852> * speed-MPS
They can also be used to describe a uniform acceleration for the aircraft of 4.5 kt/s by means of an affine relation between speed-KT and time-S:
tag relation speed-KT = 4.5 * time-S
The language also allows to describe event-driven and time-driven behaviors. The sporadic atom specifies that an event on VR-reach will occur when 55.0 is reached on speed-KT clock timeframe. Also, synchronous implies enforces that if VR-reach is triggered, so will liftoff instantaneously. In other words, the aircraft lifts off whenever airspeed reaches VR = 55 kt.
// Liftoff occurs instantaneously at rotation speed VR = 55 kt
VR-reach sporadic 55.0 on speed-KT
VR-reach implies liftoff
To achieve best performance, the pilot-in-command controls climb rate by aiming its target airspeed to Vy. To keep this model simple, we assume in a general physical model that this corresponds to a vertical speed of 1200 ft/min. Again, tag relations serve our purpose:
// Climbing with vertical speed of 1200 ft/min
tag relation altitude-FT = 1200.0 * time-MIN + -244.4
Finally, flaps retraction must occur when altitude reaches 400 ft. The time delayed implication specifies that if liftoff occurs, then the event flaps-retract will also occur at the instantaneous measured value on altitude-FT delayed by 400.0.
liftoff time delayed by 400. on altitude-FT implies flaps-retract
This execution trace depicts a satisfying run starting when time is 0 s. During acceleration at 12 s, speed has reached VR = 55 kt. Consequently, clock VR-reach is triggered and hence liftoff. The aircraft finally reaches the altitude for flaps retraction at 400 ft.