Pages

16/03/2021

Quadrilateral Speed time Curve

The simplified speed – time curve for urban and sub-urban service for electrical traction is shown in the Figure.

Quadrilateral Speed – Time Curve

The study of Quadrilateral speed time curve is given below.

Let

α = Acceleration in km per hour per second

βC = Coasting retardation in km per hour per second

β = Braking retardation in km per hour per second

V1 = Maximum speed at the end of acceleration ( km per hour )

V2 = Speed at the end of coasting period ( km per hour )

T = Total time of run ( second )

quadrilateral-speed-time-curve.png

Acceleration time in second t1 = V1 / α  …. ( 1 )

Coasting time in second t2 = V1 – V2 / βC ….. ( 2 )

Braking time in second t3 = V2 / β …… ( 3 )

Total distance travelled in ( km )

S = Distance travelled during acceleration ( Area ABC )  +

      Distance travelled during coasting ( Area BDEF ) +

      Distance travelled during retardation ( DEF )

S = ( ½ V1t1 / 3600 ) + { ( V1 + V2 ) / 2 × ( t2 / 3600 ) } + ( ½ V2t3 / 3600 )

S = ( V1t1 / 7200 ) + { ( V1t2 / 7200 ) + V2t2 / 7200 ) } + ( V2t3 / 7200 )

S = { V1 ( t1 + t2 ) / 7200 } +  { V2 ( t2 + t3 ) / 7200 }

As t1 + t2 + t3 = T

S = { V1 ( T – t3 ) / 7200 } +  { V2 ( T – t1 ) / 7200 }

S = V1T / 7200 + V2T / 7200 – V1t3 / 7200 – V2t1 / 7200

Now t = V1 / α and t3 = V2 / β

S = { T ( V1 + V2 ) / 7200 } –  ( V1 ×  V2 ) / 7200 β –  ( V1 ×  V2 ) / 7200 α

S = { T ( V1 + V2 ) / 7200 } –  V1V2 / 7200 β –  V1V2 / 7200 α

7200S = T ( V1 + V2 ) – V1V2 ( 1 / α + 1 / β )

From equation ( 2 ) 

    t2 βC = V1 – V2

    V2 = V1 – t2 βC

    V2 = V1 – βC ( T – t1 – t3 )

    V2 = V1 – βC ( T – V1 / α  – V2 / β )

    V2 = V1 – βC T + βC V1 / α +  βC V2 / β

    V2 – βC V2 / β  = V1 – βC T + βC V1 / α 

    V2 ( 1 – βC / β )  = V1 – βC ( T + V1 / α )

    V2 = V1 – βC ( T + V1 / α ) / ( 1 – βC / β ) 

You may also like :

Standard alternating voltage in India

What do you mean by low voltage, medium voltage and high voltage?

Insulation resistance of single core cable

Formula for most economical cable diameter

On which factors, the dielectric loss of cabledepends?


No comments:

Post a Comment