doc(macrorugo): update for new values of Cd0, r and fF(F)

Refs jalhyd#283

.vscode/settings.json

@@ -6,5 +6,14 @@
         "latex",
         "plaintext",
         "markdown"
+    ],
+    "cSpell.words": [
+        "Cassan",
+        "DICHO",
+        "MACRORUGO",
+        "fdescribe",
+        "jalhyd",
+        "nghyd",
+        "prms"
     ]
 }
\ No newline at end of file

docs/en/calculators/pam/macrorugo_theorie.md

@@ -4,6 +4,10 @@ The calculation of the flow rate of a rock-ramp pass corresponds to the implemen
 
 ## General calculation principle
 
+![Organigramme de la méthode de calcul](cassan2016_flow_chart_design_method.png)
+
+*After Cassan et al., 2016[^1]*
+
 There are three possibilities:
 
 - the submerged case when \(h \ge 1.1 \times k\)
@@ -106,19 +110,23 @@ $$\alpha = 1 - (a_y / a_x \times C)$$
 
 ## Formulas used
 
-### Throughput speed *V*
+### Bulk velocity *V*
 
 $$V = \frac{Q}{B \times h}$$
 
 ### Average speed between blocks *V<sub>g</sub>*
 
+From Eq. 1 Cassan et al (2016)[^1] and Eq. 1 Cassan et al (2014)[^2]:
+
 $$V_g = \frac{V}{1 - \sqrt{(a_x/a_y)C}}$$
 
 <div style="position: relative"><a id="coefficient-de-trainee-dun-bloc-cd0" style="position: absolute; top: -60px;"></a></div>
 ### Drag coefficient of a single block *C<sub>d0</sub>*
 
 \(C_{d0}\) is the drag coefficient of a block considering a single block
-infinitely high with \(F << 1\) (Cassan et al, 2016[^1]).
+infinitely high with \(F << 1\) (Cassan et al, 2014[^2]). The coefficient has been readjusted in Cassiopée version 4.14.0 from the coefficients originally proposed in Cassan et al, 2014[^2], Table 2.
+
+It is now 1.1 for a circular block and 2.6 for a flat-faced block.
 
 ### Block shape coefficient *σ*
 
@@ -126,11 +134,15 @@ Cassan et al. (2014)[^2], et Cassan et al. (2016)[^1] define \(\sigma\) as the r
 block area in the \(x,y\) plane and \(D^2\).
 For the cylindrical form of the blocks, \(\sigma\) is equal to \(\pi / 4\) and for a square block, \(\sigma = 1\).
 
-The formula used in Cassiopée has been revised to better correspond to the experimental measurements and to take into account the intermediate block shapes between circular and square.:
+### Ratio between the average speed downstream of a block and the maximum speed *r*
 
-$$ \sigma = 0.4 C_{d0} + 0.7 $$
+Cassan et al. (2014) [^2], Table 2 gives experimental measurements of this ratio for cylindrical blocks (\(r=1.2\)), rounded faces (\(r=1.2)\) and flat faces (\(r=1.5\)).
 
-We now have \(\sigma = 1.1\) for a circular block and \(\sigma = 1.5\) for a square block.
+The formula used in Cassiopeia allows to take into account shapes of intermediate blocks between circular and square shapes from the values of \(C_{d0} = 1.1\) for cylindrical blocks and \(C_{d0} = 2.6\) for blocks with flat faces:
+
+$$ r = (C_{d0} *0.4 + 1.121) / 1.5 $$
+
+We now have \(r = 1.1\) for circular blocks and \(r = 1.35\) for flat-faced blocks.
 
 ### Froude *F*
 
@@ -142,11 +154,29 @@ If \(F < 1.3\) (Eq. 5, Cassan et al., 2016)
 
 $$f_F(F) = \mathrm{min} \left( \frac{\sigma}{1- (F^2 / 4)}, \frac{1}{F^{\frac{2}{3}}} \right)^2$$
 
-else
+else (The distinction is only numerical because \(1- (F^2 / 4)\) is not defined for \(F > 2\))
 
 $$f_F(F) = F^{\frac{-4}{3}}$$
 
-(The distinction is only numerical because \(1- (F^2 / 4)\) is not defined for \(F > 2\))
+### Maximum speed *u<sub>max</sub>*
+
+According to equation 19 of Cassan et al, 2014[^2] :
+
+$$ f_F(F) = \left( \dfrac{U_d}{V_g} \right)^2 $$
+
+And equation 4:
+
+$$ \frac{u_{max}}{V_g} = r \dfrac{u_d}{V_g} $$
+
+It is deduced that :
+
+$$ u_{max} = V_g r \sqrt{f_F(F)} $$
+
+### Drag coefficient correction function linked to relative depth *f<sub>h\*</sub>(h<sub>\*</sub>)*
+
+The equation used in Cassiopeia differs slightly from Equation 20 of Cassan et al. 2014 [^2] and Equation 6 of Cassan et al. 2016 [^1]. Indeed, recent experiments have shown a better correlation with the following formula :
+
+$$ f_{h_*}(h_*) = \min \left((1 + 1 / h_*^2), 3 \right) $$
 
 ### Coefficient of friction of the bed *C<inf>f</inf>*
 

docs/fr/calculators/pam/macrorugo_theorie.md

@@ -122,9 +122,9 @@ $$V_g = \frac{V}{1 - \sqrt{(a_x/a_y)C}}$$
 
 ### Coefficient de trainée d'un bloc *C<sub>d0</sub>*
 
-\(C_{d0}\) est le coefficient de trainée d'un bloc de hauteur infinie pour un Froude \(F << 1\) (Cassan et al, 2016[^1]).
+\(C_{d0}\) est le coefficient de trainée d'un bloc de hauteur infinie pour un Froude \(F << 1\) (Cassan et al, 2014[^2]). Le coefficient a été réajusté dans la version 4.14.0 de Cassiopée par rapport aux coefficients initialement proposés dans Cassan et al, 2014[^2], Table 2.
 
-Il vaut 1 pour un plot circulaire et 2 pour un plot carré.
+Il vaut désormais 1.1 pour un bloc circulaire et 2.6 pour un plot à face plane.
 
 ### Coefficient de forme de bloc *σ*
 
@@ -135,11 +135,9 @@ On a donc \(\sigma = \pi / 4\) pour un bloc circulaire et \(\sigma = 1\) pour un
 
 Cassan et al. (2014)[^2], Table 2 donne des mesures expérimentales de ce ratio pour les blocs cylindriques (\(r=1.2\)), aux faces arrondies (\(r=1.2)\) et aux faces planes (\(r=1.5\)).
 
-La formule utilisée dans Cassiopée a été remaniée pour mieux correspondre aux mesures expérimentales et permettre une prise en compte de formes de plots intermédiaires entre les formes circulaire et carré&nbsp;:
+La formule utilisée dans Cassiopée permet une prise en compte de formes de plots intermédiaires entre les formes circulaire et carré à partir des valeurs de \(C_{d0} = 1.1\) pour les blocs cylindriques et \(C_{d0} = 2.6\) pour les blocs à faces planes&nbsp;:
 
-$$ r = 0.4 C_{d0} + 0.7 $$
-
-On a désormais \(r = 1.1\) pour un plot circulaire et \(r = 1.5\) pour un plot carré.
+$$ r = (C_{d0} *0.4 + 1.121) / 1.5 $$
 
 ### Froude *F*
 
@@ -149,7 +147,7 @@ $$F = \frac{V_g}{\sqrt{gh}}$$
 
 Si \(F < 1.3\) (Eq. 19, Cassan et al., 2014[^2])
 
-$$f_F(F) = \min \left( \frac{r}{1- F^2 / 4}, \frac{1}{F^{\frac{2}{3}}} \right)^2$$
+$$f_F(F) = \min \left( \frac{1}{1- F^2 / 4}, \frac{1}{F^{\frac{2}{3}}} \right)^2$$
 
 sinon (distinction numérique car \(\frac{r}{1- (F^2 / 4)}\) est non défini pour \(F > 2\))
 
@@ -173,7 +171,7 @@ $$ u_{max} = V_g r \sqrt{f_F(F)} $$
 
 L'équation utilisée dans Cassiopée diffère légèrement de l'équation 20 de Cassan et al. 2014[^2] et l'équation 6 de Cassan et al. 2016[^1]. En effet, les récentes expériences ont montré une meilleure corrélation avec la formule suivante :
 
-$$ f_{h_*}(h_*) = (1 + 1 / h_*^2) $$
+$$ f_{h_*}(h_*) = \min \left((1 + 1 / h_*^2), 3 \right) $$
 
 ### Coefficient de friction du lit *C<inf>f</inf>*
 

scripts/check-translations.js

@@ -4,7 +4,7 @@
  * 1) Reads Message enum in jalhyd, and for every message code in it, checks
  * that there is a translation in each nghyd's locale/*.json file (ie. for
  * every language)
- * 
+ *
  * 2) For every nghyd calculator, checks that the translated keys are the same
  * in all language files
  */
@@ -35,7 +35,7 @@ jm = jm.replace(/[ \t]+/g, "");
 // remove line breaks
 jm = jm.replace(/\n/g, "");
 
-// split on ";"
+// split on ","
 const messages = jm.split(",");
 
 // remove import on 1st line (wtf) @clodo