d7c7d17Realistic crash: plate-synthesis losses (sigma1 Laplacian term, small eta), firm 6 m/s stroke, rim 0.65 mm, strikes on the bell flank, the bow and the thin edgeJeremy Magland 1# cymbal2-crash-v1: the crash cymbal struck on the bell, on the bow and near the rim
d7c7d17Realistic crash: plate-synthesis losses (sigma1 Laplacian term, small eta), firm 6 m/s stroke, rim 0.65 mm, strikes on the bell flank, the bow and the thin edgeJeremy Magland 3The cymbal of this tier: a paraboloidal bow with a cosine-dome bell around the mounting hole and a thickness that tapers from 1.2 mm at the bell to 0.65 mm at the rim, struck three times by the stick, on the outer flank of the bell, on the bow at 0.59 R and near the rim at 0.91 R, two seconds apart. The three hits are identical sticks; what differs is the local stiffness they meet, so the ping of the bell, the tone of the bow and the crash of the thin edge come out of the same equations. The model, the strikes, the listener, the output, the error measures and the common parameters are defined in [MODEL.md](../../MODEL.md); this page fixes what is specific to this challenge. The machine-readable version is [challenge.json](challenge.json).
5## Geometry
7$$
8Z(r) = H \left( 1 - \frac{r^2}{R^2} \right) + \begin{cases} \dfrac{h_b}{2} \left( 1 + \cos \dfrac{\pi r}{r_b} \right), & r < r_b, \\[2ex] 0, & r \ge r_b, \end{cases}
9\qquad
10h(r) = \begin{cases} h_c, & r \le r_b, \\[1ex] h_c + (h_e - h_c)\, \dfrac{r - r_b}{R - r_b}, & r_b < r \le R, \end{cases}
11$$
13for $r_h \le r \le R$. The bell joins the bow with continuous slope and a jump in curvature at $r = r_b$; the thickness is continuous there.
15| Symbol | Value | Unit | Meaning |
16| --- | --- | --- | --- |
17| $H$ | 0.025 | m | bow height |
18| $r_b$ | 0.055 | m | bell radius |
19| $h_b$ | 0.015 | m | bell height above the bow |
20| $h_c$ | 0.0012 | m | thickness over the bell |
d7c7d17Realistic crash: plate-synthesis losses (sigma1 Laplacian term, small eta), firm 6 m/s stroke, rim 0.65 mm, strikes on the bell flank, the bow and the thin edgeJeremy Magland 21| $h_e$ | 0.00065 | m | thickness at the rim |
d6a9b3fTwo challenges, each with three strikes at 0, 2 and 4 s; 7 s outputJeremy Magland 22| $s_\text{ref}$ | 16 (provisional) | Pa | output scale |
d7c7d17Realistic crash: plate-synthesis losses (sigma1 Laplacian term, small eta), firm 6 m/s stroke, rim 0.65 mm, strikes on the bell flank, the bow and the thin edgeJeremy Magland 24At the three strike points the surface is 25, 16 and 4 mm above the rim plane, its slope is 0.29, 0.15 and 0.22, and the thickness is 1.20, 0.96 and 0.72 mm; the first footprint spans 40 to 50 mm from the axis, on the bell, and the third 180 to 190 mm, 13 mm from the rim. The largest slope of the profile is about 0.46, on the flank of the bell, where shallow-shell theory is a coarse approximation of a real cymbal; the model is nevertheless defined as written.