# Model Mathematics

### Component: F_SE

$F_SE=cT⁢F_max⁢kT⁢ln⁡ⅇLT-LT_rkT+1$

### Component: F_PE1

$F_PE1=c1⁢k1⁢ln⁡ⅇLL_max-L_r1k1+1+eta⁢V$

### Component: F_PE2

$F_PE2=c2⁢ⅇk2⁢L-L_r2-1$

### Component: FL

$FL=ⅇ-|Lbeta-1omega|rho$

### Component: FV

$FV=V_max-VV_max+cv0+cv1⁢L⁢VifV≦0bv-av0+av1⁢L+av2⁢L2⁢Vbv+Votherwise$

### Component: Af

$Af=1-ⅇ-Y⁢S⁢f_effaf⁢nfnf$

### Component: F0

$F0=Af⁢FL+FV+F_PE2+F_PE1$

### Component: F_CE

$F_CE=F0⁢F_max$

### Component: F_total

$F_total=F_SE-F_CE$

### Component: L_eff

$ddtimeL_eff=L-L_eff3T_L⁢1-Af$

### Component: S

$ddtimeS=as_-ST_sas_=as1iff_eff<0.1as2otherwise$

### Component: Y

$ddtimeY=1-c_Y⁢1-ⅇ-|V|V_Y+YT_Y$

### Component: rise_and_fall_time

$ddtimef_int=f_env-f_intT_fddtimef_eff=df_eff_dtdf_eff_dt=f_int-f_effT_fT_f=T_f1⁢L2+T_f2⁢f_envifdf_eff_dt≥0T_f3+T_f4⁢AfLotherwise$

### Component: V

$ddtimeV=F_total1⁢mass$

### Component: V0

$V0=VL_max$

### Component: L0

$L0=LL_max$

### Component: L

$ddtimeL=V$

### Component: user_defined_constants

Source
Derived from workspace Cheng, Brown, Loeb, 2000 at changeset 793a1c2df2bf.
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