diff --git a/module_04/mlb_torpedo-bats.ipynb b/module_04/mlb_torpedo-bats.ipynb new file mode 100644 index 0000000..ffe80e5 --- /dev/null +++ b/module_04/mlb_torpedo-bats.ipynb @@ -0,0 +1,900 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c1427231-f544-4580-92bf-36a8fb14ab25", + "metadata": {}, + "source": [ + "# Comparing Physics and Performance of Traditional vs. Torpedo Bats" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "c772f519-b6fd-418c-8743-170e8a22af61", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "e8d7c87c-6d0d-4f30-b2c5-1aeeb8971955", + "metadata": {}, + "source": [ + "## Introduction:\n", + "Recently in Major League Baseball, a new bat design has emerged, being called the \n", + "“Torpedo Bat”. Traditional baseball bats have a continuous taper, with the radius getting \n", + "gradually larger from the handle to the tip. Torpedo bats, as opposed to traditional baseball \n", + "bats, have moved some of the mass from the end of the bat toward the handle. In other \n", + "words, the torpedo bats reach the area of maximum radius sooner than traditional bats and \n", + "then taper off smaller toward the end. This gives the torpedo bats a distinctive “bowling \n", + "pin” shape, with the maximum radius about 6-7 inches from the bats tip. The intent in the \n", + "design of these bats is to move the center of mass of the bat closer to the handle, to account \n", + "for players that typically contact the ball further from the tip of the bat. \n", + "\n", + "This report focuses on physics in how the differing mass distributions (including \n", + "where the center of mass is located) and contact locations (point at which the ball impacts \n", + "the bat) affect the exit velocity of the baseball after contact. Exit velocity is critical for \n", + "hitters’ performance, as a exit velocity has the greatest impact on a player’s batting average. \n", + "Batting average is a batters’ hits (batting the pitch in play and reaching base safely) divided \n", + "by at bats (plate appearances that result in either a hit or an out, which removes walks from \n", + "the equation). To showcase how much exit velocity has an impact on batting average, we \n", + "can look at the correlation between the two in Major League Baseball. Balls hit at 95 miles \n", + "per hour (MPH) have a batting average of 0.265, whereas balls hit at 96 MPH have a batting \n", + "average of just over 0.300. This jump of 0.035 over just one MPH is big in baseball, where \n", + "batters have an average of 500-600 at bats per season. This means that jumping from 95 \n", + "MPH exit velocity to 96 MPH exit velocity translates to approximately 17.5-21 more hits \n", + "each season. With the mass distribution having a great impact on swing speed, and swing \n", + "speed and contact location having the largest impact on exit velocity, this report will be \n", + "looking at how these two types of bats compare to one another.\n", + "\n", + "## Maximum Radius and Mass Distribution Comparison\n", + "In order to make a fair comparison between the two bat types (to focus solely on bat \n", + "design), the length of each bat will be kept constant at 34 inches. Also for this analysis, we \n", + "will be considering the maximum diameter of the torpedo bat to be 6 inches from the end \n", + "(opposite of the handle) of the bat, consistent with averages of these bat types. Finally, also \n", + "going with averages across the MLB, the maximum diameter of the traditional versus \n", + "torpedo bats will be considered to be 1.250 inches and 1.305 inches (maximum allowable \n", + "\n", + "\n", + "radius per MLB regulations) respectively. Taking all of this in to account, we can model the \n", + "mass distributions of the two bat types as shown in Figure 1 below.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "2ad08905-a53b-40c9-a438-49f26c9010e1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Figure 1. Bat Geometry & Radius Profiles\n", + "\n", + "length = 34 # Bat length in inches\n", + "\n", + "x = np.linspace(0, length, 500) # 0 = tip, length = handle knob\n", + "\n", + "# Standard bat: linear taper from max barrel radius to handle radius\n", + "\n", + "r_std = np.interp(x, [0, 8, length], [1.25, 1.00, 0.50])\n", + "\n", + "# Torpedo bat: bulge near mid-barrel (6\" from tip), then taper\n", + "\n", + "bulge_center = 6\n", + "\n", + "bulge_width = 4\n", + "\n", + "r_torp = np.interp(x,[0,bulge_center - bulge_width/2, bulge_center,\n", + "bulge_center + bulge_width/2, length], [1.00, 1.00, 1.305, 1.00,\n", + "0.50])\n", + "\n", + "# Plot radius profiles\n", + "\n", + "plt.figure(figsize=(8, 4))\n", + "\n", + "plt.plot(x, r_std, label='Standard Bat')\n", + "\n", + "plt.plot(x, r_torp, label='Torpedo Bat')\n", + "\n", + "plt.xlabel('Distance from Tip (in)')\n", + "\n", + "plt.ylabel('Radius (in)')\n", + "\n", + "plt.title('Bat Radius Profile')\n", + "\n", + "plt.legend()\n", + "\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "de600cdd-8227-435a-be5a-d05e3321a9ba", + "metadata": {}, + "source": [ + "As expected, we see the radius of the torpedo bat peak at six inches from the tip and \n", + "taper off both ways, with the traditional bat peaking at the tip and tapering down to the \n", + "handle. Using this radius distribution, it is now possible to calculate the total mass as well as\n", + "map out the mass distribution of each of the two bat types. We will be considering both bats \n", + "to be made of maple, the most common material for MLB bats to be made of. For this reason, \n", + "the density used in the model will be 0.375 ounces per cubic inch, the average for maple \n", + "bats. Using this density, the mass of the traditional bat is found to be 29.85 ounces, and the \n", + "mass of the torpedo bat is 28.88 ounces -- a 0.97 ounce (or 3.3%) reduction from \n", + "traditional. The mass distribution comparison can be seen below:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "13cc84c3-4988-4a52-876c-7fa3963e789f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Center of mass (0–28 in) Standard bat: 10.90 in from tip\n", + "Center of mass (0–28 in) Torpedo bat: 11.41 in from tip\n" + ] + } + ], + "source": [ + "# Figure 2: Mass Distributions and COM\n", + "\n", + "# Material density\n", + "\n", + "density = 0.375 # ounces per cubic inch\n", + "\n", + "# Cross-sectional areas (in²)\n", + "\n", + "A_std = np.pi * r_std**2\n", + "\n", + "A_torp = np.pi * r_torp**2\n", + "\n", + "# Linear mass distributions (oz per inch)\n", + "\n", + "m_lin_std = density * A_std\n", + "\n", + "m_lin_torp = density * A_torp\n", + "\n", + "# Integrate to find total mass (oz)\n", + "\n", + "mass_std = np.trapz(m_lin_std, x)\n", + "\n", + "mass_torp = np.trapz(m_lin_torp, x)\n", + "\n", + "# Truncate to 0–28 inches from tip\n", + "\n", + "cutoff = 28 # inches\n", + "\n", + "mask = x <= cutoff\n", + "\n", + "# Compute truncated total mass (optional)\n", + "\n", + "mass_std_trunc = np.trapz(m_lin_std[mask], x[mask])\n", + "\n", + "mass_torp_trunc = np.trapz(m_lin_torp[mask], x[mask])\n", + "\n", + "# Compute truncated center of mass (inches from tip)\n", + "\n", + "com_std_trunc = np.trapz(x[mask] * m_lin_std[mask], x[mask]) /mass_std_trunc\n", + "\n", + "com_torp_trunc = np.trapz(x[mask] * m_lin_torp[mask], x[mask]) /mass_torp_trunc\n", + "\n", + "# Print center of mass values\n", + "\n", + "print(f\"Center of mass (0–28 in) Standard bat: {com_std_trunc:.2f} in from tip\")\n", + "\n", + "print(f\"Center of mass (0–28 in) Torpedo bat: {com_torp_trunc:.2f} in from tip\")" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "2f54770f-3db4-424b-b6c5-1082927c90b1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total mass of standard bat: 29.85 oz\n", + "Total mass of torpedo bat: 28.88 oz\n" + ] + } + ], + "source": [ + "# Plot the mass distributions with COM color-matched\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "line_std, = plt.plot(x, m_lin_std, \n", + " label='Standard Bat',\n", + " linewidth=2, \n", + " color='orange')\n", + "\n", + "line_torp, = plt.plot(x, m_lin_torp, \n", + " label='Torpedo Bat', \n", + " linewidth=2)\n", + "\n", + "# Retrieve distribution colors\n", + "\n", + "color_std = line_std.get_color()\n", + "\n", + "color_torp = line_torp.get_color()\n", + "\n", + "# Plot COM and cutoff \n", + "\n", + "plt.axvline(com_std_trunc, linestyle='--', color=color_std,\n", + "linewidth=1.5, label='COM Std (0–28 in)')\n", + "\n", + "plt.axvline(com_torp_trunc, linestyle='--', color=color_torp,\n", + "linewidth=1.5, label='COM Torp (0–28 in)')\n", + "\n", + "plt.axvline(cutoff, linestyle=':', \n", + " color='red', \n", + " linewidth=1.5, \n", + " label='COM Cutoff at 28 in')\n", + "\n", + "# Labels and styling\n", + "\n", + "plt.xlabel('Distance from Tip (inches)')\n", + "\n", + "plt.ylabel('Linear Mass Distribution (oz/in)')\n", + "\n", + "plt.title('Mass Distribution & Truncated Center of Mass (0–28 in) Comparison')\n", + "\n", + "plt.legend()\n", + "\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "plt.show()\n", + "\n", + "print(f\"Total mass of standard bat: {mass_std:.2f} oz\")\n", + "\n", + "print(f\"Total mass of torpedo bat: {mass_torp:.2f} oz\")" + ] + }, + { + "cell_type": "markdown", + "id": "985f76ce-0af8-43ca-b0b1-f80f2e1e4811", + "metadata": {}, + "source": [ + "Finally, we can see where the center of mass (COM) of each bat is based on the mass \n", + "distributions. For these calculations, we disregard the initial six inches from the handle \n", + "know (28-34 on the graph), as this is the region where the bat is held from. Therefore, it \n", + "should not be used to calculate the COM or factor into the future moment of inertia \n", + "calculations. That being said, the truncated COM of the traditional bat sits at 10.90 inches \n", + "from the tip and the torpedo bat COM is 0.51 inches further toward the hands, at 11.41 \n", + "inches from the tip." + ] + }, + { + "cell_type": "markdown", + "id": "d99bb463-016c-40e8-9e16-4fe14976eff1", + "metadata": {}, + "source": [ + "## Swing Speed Comparison\n", + "Now that the truncated center of mass has been calculated for both the traditional \n", + "and torpedo bats, it can be used to find the moment of inertia (MOI) about the pivot points \n", + "for each bat. The pivot point is six inches from the handle knob, which is the industry \n", + "standard for measuring moment of inertia of a baseball bat." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "68b3bf6c-c3ea-4b79-8659-890bf18b4f9e", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'com_std' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[34], line 3\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m# Compute I_COM via integration about each COM (oz·in²)\u001b[39;00m\n\u001b[0;32m----> 3\u001b[0m I_com_std \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mtrapz(m_lin_std \u001b[38;5;241m*\u001b[39m (x \u001b[38;5;241m-\u001b[39m \u001b[43mcom_std\u001b[49m)\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m, x)\n\u001b[1;32m 5\u001b[0m I_com_torp \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mtrapz(m_lin_torp \u001b[38;5;241m*\u001b[39m (x \u001b[38;5;241m-\u001b[39m com_torp)\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m, x)\n\u001b[1;32m 7\u001b[0m \u001b[38;5;66;03m# Pivot point at 6 inches from the handle knob\u001b[39;00m\n", + "\u001b[0;31mNameError\u001b[0m: name 'com_std' is not defined" + ] + } + ], + "source": [ + "# Compute I_COM via integration about each COM (oz·in²)\n", + "\n", + "I_com_std = np.trapz(m_lin_std * (x - com_std)**2, x)\n", + "\n", + "I_com_torp = np.trapz(m_lin_torp * (x - com_torp)**2, x)\n", + "\n", + "# Pivot point at 6 inches from the handle knob\n", + "\n", + "pivot_x = length - 6 # inches from handle knob\n", + "\n", + "# Distance from pivot to COM (inches)\n", + "\n", + "r_COM_std_pivot = abs(pivot_x - com_std)\n", + "\n", + "r_COM_torp_pivot = abs(pivot_x - com_torp)\n", + "\n", + "# Moment of inertia about pivot (oz·in²)\n", + "\n", + "I_pivot_std = I_com_std + mass_std * r_COM_std_pivot**2\n", + "\n", + "I_pivot_torp = I_com_torp + mass_torp * r_COM_torp_pivot**2\n", + "\n", + "# Print results\n", + "\n", + "print(f\"Pivot point: {pivot_x:.2f} in from tip\")\n", + "\n", + "print(\"Standard Bat:\")\n", + "\n", + "print(f\" I_pivot: {I_pivot_std:.4f} oz·in²\")\n", + "\n", + "print(\"\\nTorpedo Bat:\")\n", + "\n", + "print(f\" I_pivot: {I_pivot_torp:.4f} oz·in²\")" + ] + }, + { + "cell_type": "markdown", + "id": "7d0c2358-d7ad-4d2a-9801-4628d3c960c2", + "metadata": {}, + "source": [ + "The MOI is found to be 11257.49 oz·in² for the traditional bat, and 10289.36 oz·in²\n", + "for the torpedo bat. The torpedo bat MOI being lower (a 968.03 oz·in², or 8.6% reduction) \n", + "than traditional is what we expect to see, with more mass being closer to the pivot point. \n", + "These values, along with the researched value for average MLB players torque applied \n", + "about the to the pivot point and the average arc length (angle through which the bats are \n", + "swung through), can now be used to calculate the average swing speeds for each bat type. \n", + "For calculating the swing speed, it will be based on the “sweet spot” location. This is the \n", + "location in which the exit velocity should be peaked, which is located approximately \n", + "halfway between the COM and the tip (opposite of the handle) for each bat." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "07a13e03-4812-4a73-8149-6a0a637ecbda", + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "unterminated string literal (detected at line 57) (4081135871.py, line 57)", + "output_type": "error", + "traceback": [ + "\u001b[0;36m Cell \u001b[0;32mIn[16], line 57\u001b[0;36m\u001b[0m\n\u001b[0;31m print(f\"Average Standard Bat Speed at Sweet Spot: {v_std_avg:.1f}\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m unterminated string literal (detected at line 57)\n" + ] + } + ], + "source": [ + "# 4. Impact radius (sweet spot halfway to COM)\n", + "\n", + "r_imp_std_in = abs(pivot_x - com_std/2)\n", + "\n", + "r_imp_torp_in = abs(pivot_x - com_torp/2)\n", + "\n", + "# 5. Energy‐based swing model\n", + "\n", + "arc_length_ft = 7.3 # ft\n", + "\n", + "r_imp_std_ft = r_imp_std_in / 12\n", + "\n", + "r_imp_torp_ft = r_imp_torp_in / 12\n", + "\n", + "theta_std = arc_length_ft / r_imp_std_ft\n", + "\n", + "theta_torp = arc_length_ft / r_imp_torp_ft\n", + "\n", + "# 6. Torque for average swing speed\n", + "\n", + "tau_avg = 10897.03 # in·oz\n", + "\n", + "# Conversion factors\n", + "\n", + "in_oz_to_lbf_ft = 1 / (16 * 12) # in·oz → lbf·ft\n", + "\n", + "oz_in2_to_slug_ft2 = (1/16) * (1/144) / 32.174 # oz·in² → slug·ft²\n", + "\n", + "mph_factor = (1/12) * 0.681818 # in/s → mph\n", + "\n", + "# 7. Compute average speeds\n", + "\n", + "def speed_mph(tau_oz_in, theta, I_pivot_oz_in2, r_imp_in):\n", + "\n", + "# convert units internally\n", + "\n", + "tau_lbf_ft = tau_oz_in * in_oz_to_lbf_ft\n", + "\n", + "I_slug_ft2 = I_pivot_oz_in2 * oz_in2_to_slug_ft2\n", + "\n", + "omega = np.sqrt(2 * tau_lbf_ft * theta / I_slug_ft2)\n", + "\n", + "v_in_s = omega * r_imp_in\n", + "\n", + "return v_in_s * mph_factor\n", + "\n", + "# Calculate average swing speeds\n", + "\n", + "v_std_avg = speed_mph(tau_avg,\n", + "theta_std, I_pivot_std, r_imp_std_in)\n", + "\n", + "v_torp_avg = speed_mph(tau_avg, theta_torp, I_pivot_torp,\n", + "r_imp_torp_in)\n", + "\n", + "# 8. Output\n", + "\n", + "print(f\"Average Standard Bat Speed at Sweet Spot: {v_std_avg:.1f}\n", + "mph\")\n", + "\n", + "print(f\"Average Torpedo Bat Speed at Sweet Spot: {v_torp_avg:.1f}\n", + "mph\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "ffc1b897-3cb4-418b-82ca-b882eb330545", + "metadata": {}, + "source": [ + "This gives us that the speed at the sweet spot for the traditional bat is 69.0 MPH, and \n", + "the torpedo bat is 71.8 MPH. This is a noticeable jump of 2.8 MPH (4.1% gain), showcasing \n", + "the swing speed advantages of the torpedo bats. We can further visualize this swing speed \n", + "difference with the bar chart below." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "09b607f9-8dc8-4a76-90d5-702f23c71cec", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'r_imp_std_in' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[19], line 7\u001b[0m\n\u001b[1;32m 3\u001b[0m n_samples \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m100\u001b[39m\n\u001b[1;32m 5\u001b[0m \u001b[38;5;66;03m# build the r_imp ranges\u001b[39;00m\n\u001b[0;32m----> 7\u001b[0m r_std_range \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[43mr_imp_std_in\u001b[49m \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m3\u001b[39m, \n\u001b[1;32m 8\u001b[0m r_imp_std_in \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m3\u001b[39m,\n\u001b[1;32m 9\u001b[0m n_samples)\n\u001b[1;32m 11\u001b[0m r_torp_range \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(r_imp_torp_in \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m3\u001b[39m, \n\u001b[1;32m 12\u001b[0m r_imp_torp_in \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m3\u001b[39m,\n\u001b[1;32m 13\u001b[0m n_samples)\n\u001b[1;32m 15\u001b[0m \u001b[38;5;66;03m# vectorized speed calls\u001b[39;00m\n", + "\u001b[0;31mNameError\u001b[0m: name 'r_imp_std_in' is not defined" + ] + } + ], + "source": [ + "# --- Error‐bar analysis over r_imp = COM/2 ± 3 in ---\n", + "\n", + "n_samples = 100\n", + "\n", + "# build the r_imp ranges\n", + "\n", + "r_std_range = np.linspace(r_imp_std_in - 3, \n", + " r_imp_std_in + 3,\n", + " n_samples)\n", + "\n", + "r_torp_range = np.linspace(r_imp_torp_in - 3, \n", + " r_imp_torp_in + 3,\n", + " n_samples)\n", + "\n", + "# vectorized speed calls\n", + "\n", + "v_std_samples = speed_mph(tau_avg, \n", + " theta_std, \n", + " I_pivot_std, \n", + " r_std_range)\n", + "\n", + "v_torp_samples = speed_mph(tau_avg, \n", + " theta_torp, \n", + " I_pivot_torp,\n", + " r_torp_range)\n", + "\n", + "# compute statistics\n", + "\n", + "v_std_mean, v_std_std = np.mean(v_std_samples), np.std(v_std_samples)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "4b6ad811-0522-4e03-a5a3-badfb1e8a8e7", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'v_torp_samples' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[20], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m v_torp_mean, v_torp_std \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mmean(\u001b[43mv_torp_samples\u001b[49m),\n\u001b[1;32m 2\u001b[0m np\u001b[38;5;241m.\u001b[39mstd(v_torp_samples)\n\u001b[1;32m 4\u001b[0m \u001b[38;5;66;03m# plot bar chart with error bars\u001b[39;00m\n", + "\u001b[0;31mNameError\u001b[0m: name 'v_torp_samples' is not defined" + ] + } + ], + "source": [ + "v_torp_mean, v_torp_std = np.mean(v_torp_samples),\n", + "np.std(v_torp_samples)\n", + "\n", + "# plot bar chart with error bars\n", + "\n", + "plt.figure(figsize=(6,4))\n", + "\n", + "labels = ['Standard', 'Torpedo']\n", + "\n", + "means = [v_std_mean, v_torp_mean]\n", + "\n", + "errs = [v_std_std, v_torp_std]\n", + "\n", + "plt.bar(labels, means, yerr=errs, capsize=5)\n", + "\n", + "plt.ylabel('Swing Speed (mph)')\n", + "\n", + "plt.title('Mean Swing Speed ± Std Dev (r_imp = COM/2 ± 3″)')\n", + "\n", + "plt.grid(axis='y', linestyle='--', alpha=0.6)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "42bb19d9-e4ec-4ab2-bb19-3d194b0e482d", + "metadata": {}, + "source": [ + "The bar chart shows both the swing speeds of both bats at the “sweet spot”, as well \n", + "as error bars. These error bars showcase the swing speed at +/- 3 inches from the sweet \n", + "spot location, accounting for variability in contact location. \n", + "\n", + "## Exit Velocity Comparison\n", + "Using all of the data we have calculated above (bat radius profile, mass distributions, \n", + "swings speeds, etc.), we can finally create a program to model the differences in exit velocities between the two bats. For this, we will be considering the baseball to have a mass \n", + "of 5.125 ounces and the pitch speeds to be 90 MPH, in order to solely focus on bat design\n", + "and performance. A Monte Carlo simulation can be run to model the exit velocities, with \n", + "variations in the contact location, as well as swing speeds (variation is directly related to \n", + "contact location). It also takes into account the variability of coefficient of restitution (e) of \n", + "the ball-bat collision with contact location, using a sampling from a normal distribution to \n", + "reflect this. For the normal distribution of e, the mean is 0.489 and the standard deviation is \n", + "0.009, reflecting averages from maple bat coefficient of restitution data.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "2c5e8296-d160-4d22-bfe9-539167f9bb38", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'I_pivot_std' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[25], line 33\u001b[0m\n\u001b[1;32m 27\u001b[0m m_ball \u001b[38;5;241m=\u001b[39m m_ball_oz \u001b[38;5;241m*\u001b[39m oz_to_slug \u001b[38;5;66;03m# slug\u001b[39;00m\n\u001b[1;32m 29\u001b[0m \u001b[38;5;66;03m# 3. Precompute bat effective masses (slug) at the _mean_ sweet spot\u001b[39;00m\n\u001b[1;32m 30\u001b[0m \n\u001b[1;32m 31\u001b[0m \u001b[38;5;66;03m# (we’ll recompute on the fly for each r_imp_sample below)\u001b[39;00m\n\u001b[0;32m---> 33\u001b[0m m_eff_std \u001b[38;5;241m=\u001b[39m (\u001b[43mI_pivot_std\u001b[49m \u001b[38;5;241m/\u001b[39m (r_imp_std_in\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m)) \u001b[38;5;241m*\u001b[39m oz_to_slug\n\u001b[1;32m 35\u001b[0m m_eff_torp\u001b[38;5;241m=\u001b[39m (I_pivot_torp \u001b[38;5;241m/\u001b[39m (r_imp_torp_in\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m)) \u001b[38;5;241m*\u001b[39m oz_to_slug\n\u001b[1;32m 37\u001b[0m \u001b[38;5;66;03m# 4. Sample contact locations\u001b[39;00m\n", + "\u001b[0;31mNameError\u001b[0m: name 'I_pivot_std' is not defined" + ] + } + ], + "source": [ + "# 1. Simulation parameters\n", + "\n", + "m_ball_oz = 5.125 # ball mass (oz)\n", + "\n", + "pitch_speed_mph = 90 # pitch speed (mph)\n", + "\n", + "N_samples = 10000 # number of Monte Carlo draws\n", + "\n", + "# --- Sample COR from distribution ---\n", + "\n", + "mean_e = 0.489 # average wood-bat COR from Nathan et al. (2011)\n", + "\n", + "sigma_e = 0.009 # std. dev. from Nathan et al. (2011)\n", + "\n", + "e_samps = np.random.normal(mean_e, sigma_e, N_samples)\n", + "\n", + "e_samps = np.clip(e_samps, 0, 1) # ensure 0 ≤ e ≤ 1\n", + "\n", + "# 2. Unit conversions\n", + "\n", + "mph_to_fps = 5280/3600 # ft/s per mph\n", + "\n", + "oz_to_slug = (1/16) / 32.174 # oz → lbm → slugs\n", + "\n", + "v_pitch = -pitch_speed_mph * mph_to_fps # ft/s (negative = toward bat)\n", + "\n", + "m_ball = m_ball_oz * oz_to_slug # slug\n", + "\n", + "# 3. Precompute bat effective masses (slug) at the _mean_ sweet spot\n", + "\n", + "# (we’ll recompute on the fly for each r_imp_sample below)\n", + "\n", + "m_eff_std = (I_pivot_std / (r_imp_std_in**2)) * oz_to_slug\n", + "\n", + "m_eff_torp= (I_pivot_torp / (r_imp_torp_in**2)) * oz_to_slug\n", + "\n", + "# 4. Sample contact locations\n", + "\n", + "r_std_samps = np.random.uniform(r_imp_std_in - 3, r_imp_std_in + 3, N_samples)\n", + "\n", + "r_torp_samps = np.random.uniform(r_imp_torp_in - 3, r_imp_torp_in + 3, N_samples)\n", + "\n", + "# 5. Compute swing speeds (mph → ft/s)\n", + "\n", + "v_std_mph_samps = speed_mph(tau_avg,theta_std, I_pivot_std, r_std_samps)\n", + "\n", + "v_torp_mph_samps = speed_mph(tau_avg, theta_torp, I_pivot_torp,r_torp_samps)\n", + "\n", + "v_std_samps = v_std_mph_samps * mph_to_fps\n", + "\n", + "v_torp_samps = v_torp_mph_samps * mph_to_fps\n", + "\n", + "# --- Compute exit velocities with variable e ---\n", + "\n", + "v_exit_std = (m_eff_std * v_std_samps+ m_ball * v_pitch+ m_eff_std * e_samps * (v_std_samps - v_pitch)) / (m_eff_std + m_ball)\n", + "\n", + "v_exit_torp = (m_eff_torp * v_torp_samps+ m_ball * v_pitch+ m_eff_torp * e_samps *(v_torp_samps - v_pitch)) / (m_eff_torp + m_ball)\n", + "\n", + "# 7. Back to mph\n", + "\n", + "v_exit_std_mph = v_exit_std / mph_to_fps\n", + "\n", + "v_exit_torp_mph = v_exit_torp / mph_to_fps\n", + "\n", + "# 8. Plot histograms\n", + "\n", + "plt.figure(figsize=(8,5))\n", + "\n", + "plt.hist(v_exit_std_mph, bins=50, alpha=0.6, label='Standard')\n", + "\n", + "plt.hist(v_exit_torp_mph, bins=50, alpha=0.6, label='Torpedo')\n", + "\n", + "plt.xlabel('Exit Velocity (mph)')\n", + "\n", + "plt.ylabel('Count')\n", + "\n", + "plt.title('Monte Carlo Exit Velocity (contact ±3″)')\n", + "\n", + "plt.legend()\n", + "\n", + "plt.tight_layout()\n", + "\n", + "plt.show()\n", + "\n", + "# 9. Print mean ± 2σ\n", + "\n", + "std_mu, std_sigma = np.mean(v_exit_std_mph), np.std(v_exit_std_mph)\n", + "\n", + "torp_mu, torp_sigma = np.mean(v_exit_torp_mph), np.std(v_exit_torp_mph)\n", + "\n", + "print(f\"Standard bat exit: {std_mu:.1f} ± {2*std_sigma:.1f} mph (2σ)\")\n", + "\n", + "print(f\"Torpedo bat exit: {torp_mu:.1f} ± {2*torp_sigma:.1f} mph (2σ)\")" + ] + }, + { + "cell_type": "markdown", + "id": "b8d78e16-0b69-4a48-8529-eeb199ad5a72", + "metadata": {}, + "source": [ + "In the histogram, we can see that the data for the torpedo bats is shifted right \n", + "(toward higher exit velocities) as compared to the traditional bats. The exit velocities (mean \n", + "± 2σ) for each of the two bats are: 102.4 ± 12.9 mph (traditional), 103.0 ± 13.6 mph \n", + "(torpedo). Although they are close, the 0.6 increase in mean exit velocity shows the effect on \n", + "performance that the torpedo bat brings. We can now take a look at how both exit velocity \n", + "and coefficient of restitution vary with contact location in the figure below. \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "822f4a30-77b7-4d84-9dc0-643f62ff208f", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'pivot_x' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[30], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m x_ss_std \u001b[38;5;241m=\u001b[39m \u001b[43mpivot_x\u001b[49m \u001b[38;5;241m-\u001b[39m com_std\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m2\u001b[39m\n\u001b[1;32m 3\u001b[0m x_ss_torp \u001b[38;5;241m=\u001b[39m pivot_x \u001b[38;5;241m-\u001b[39m com_torp\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m2\u001b[39m\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21me_profile\u001b[39m(x_tip, x_center, sigma\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2.0\u001b[39m, e0\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.489\u001b[39m):\n", + "\u001b[0;31mNameError\u001b[0m: name 'pivot_x' is not defined" + ] + } + ], + "source": [ + "x_ss_std = pivot_x - com_std/2\n", + "\n", + "x_ss_torp = pivot_x - com_torp/2\n", + "\n", + "def e_profile(x_tip, x_center, sigma=2.0, e0=0.489):\n", + " \"\"\"Gaussian COR profile vs. contact-location x_tip (inches from tip).\"\"\"\n", + " return e0 * np.exp(-0.5*((x_tip - x_center)/sigma)**2)\n", + "\n", + "# 1) sample your impact‐locations in tip‐coordinates\n", + "\n", + "x_tip = np.linspace(0, pivot_x, 500)\n", + "\n", + "# 2) convert to lever arm\n", + "\n", + "r_imp = pivot_x - x_tip\n", + "\n", + "# 3) get swing speeds\n", + "\n", + "v_std_mph = speed_mph(tau_avg, theta_std, I_pivot_std, r_imp)\n", + "\n", + "v_torp_mph = speed_mph(tau_avg, theta_torp, I_pivot_torp, r_imp)\n", + "\n", + "v_std_fps = v_std_mph * mph_to_fps\n", + "\n", + "v_torp_fps = v_torp_mph * mph_to_fps\n", + "\n", + "# 4) effective mass (slugs)\n", + "\n", + "m_eff_std = (I_pivot_std * oz_in2_to_slug_ft2)/((r_imp/12)**2)\n", + "\n", + "m_eff_torp = (I_pivot_torp * oz_in2_to_slug_ft2)/((r_imp/12)**2)\n", + "\n", + "# 5) COR curves\n", + "\n", + "e_std_curve = e_profile(x_tip, x_ss_std, sigma=2.0, e0=0.489)\n", + "\n", + "e_torp_curve = e_profile(x_tip, x_ss_torp, sigma=2.0, e0=0.489)\n", + "\n", + "# 6) exit‐velocity formula (ft/s)\n", + "\n", + "v_exit_std = (\n", + "\n", + "m_eff_std * v_std_fps\n", + "\n", + "+ m_ball * v_pitch\n", + "\n", + "+ m_eff_std * e_std_curve * (v_std_fps - v_pitch)\n", + "\n", + ")/(m_eff_std + m_ball)\n", + "\n", + "v_exit_torp= (\n", + "\n", + "m_eff_torp * v_torp_fps\n", + "\n", + "+ m_ball * v_pitch\n", + "\n", + "+ m_eff_torp * e_torp_curve * (v_torp_fps - v_pitch)\n", + "\n", + ")/(m_eff_torp + m_ball)\n", + "\n", + "# back to mph\n", + "\n", + "v_exit_std_mph = v_exit_std / mph_to_fps\n", + "\n", + "v_exit_torp_mph = v_exit_torp / mph_to_fps\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "fig, ax = plt.subplots(figsize=(8,5))\n", + "\n", + "ax.plot(x_tip, v_exit_std_mph, color='red', \n", + " label='Traditional Bat', linewidth=2)\n", + "\n", + "ax.plot(x_tip, v_exit_torp_mph, color='blue', \n", + " label='Torpedo Bat', linewidth=2)\n", + "\n", + "ax.set_xlim(0, pivot_x)\n", + "\n", + "ax.set_xlabel('Distance from Pivot Point (inches)')\n", + "\n", + "ax.set_ylabel('Exit Velocity (mph)')\n", + "\n", + "ax.set_title('Exit Velocity vs Impact Location\\n(with location-dependent COR)')\n", + "\n", + "ax.legend()\n", + "\n", + "ax.grid(True, linestyle='--', alpha=0.3)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "224a1e6c-9156-4c76-adf5-e6c418780caf", + "metadata": {}, + "source": [ + "From this, it is apparent that the torpedo bat’s curve sits ~1 inch closer to the pivot \n", + "point than the traditional bat’s curve, matching its slightly more inward sweet spot. Also, its \n", + "maximum exit velocity at that peak is noticeably higher (By about 3.5 MPH), reflecting the \n", + "lower moment of inertia you built into the torpedo design. This tells us that if you can \n", + "consistently hit the torpedo bat’s sweet spot, you’ll get a measurable boost in exit velocity.\n", + "\n", + "## Conclusion\n", + "Torpedo bats weigh 28.88 oz versus 29.85 oz for traditional bats (−3.3%), with the \n", + "center of mass shifting from 10.90 inches to 11.41 inches from the tip and moment of inertia \n", + "about a 6 inch pivot dropping by 8.6% (11,257.5 → 10,289.4 oz·in²) . This mass \n", + "redistribution boosts sweet-spot swing speed from 69.0 mph to 71.8 mph (+4.1%) and \n", + "raises mean exit velocity under a 90 MPH pitch by 0.6 MPH (102.4 → 103.0 mph) . This \n", + "boost in exit velocity is crucial for players, as stated in the introduction, as any increase can \n", + "have a great enhancement on players performance metrics. To wrap up, if a player is precise \n", + "in their contact location, the torpedo bats can give a significant boost to player’s hitting \n", + "success. \n", + "\n", + "## Sources\n", + "1. https://sports.yahoo.com/mlb/article/how-to-assess-the-impact-of-a-torpedo-bat-\n", + "these-are-the-stats-to-look-at-\n", + "211347005.html?guccounter=1&guce_referrer=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_sig=AQAAAAl3NQzBYIJ_3ACKX9TRlv19lImSI141GTuUgw8YiN\n", + "K9Yu0N8RvjWMj9KWVfZ5-\n", + "3pTQADO68rAda37hd1ih8Sqh8mgMqLRDRo9JggwbsdmTLYGNlWkKbZu8z-\n", + "cdGr1VQW4vIQyhFqGLBi31-NRWkCDJZlS6DTNqD9dUAu5S3Lwd5\n", + "2. https://blogs.fangraphs.com/the-physics-of-the-torpedo-bat/\n", + "3. https://winreality.com/blog/exit-velo-by-\n", + "age/#:~:text=Simply%20put%2C%20the%20harder%20a,300.\n", + "4. https://pebblehunting.substack.com/p/imagine-an-enormous-bat-barrel\n", + "5. https://www.physics.usyd.edu.au/~cross/baseball.html\n", + "6. https://baseballrulesacademy.com/official-rule/mlb/3-02-1-10-\n", + "bat/#google_vignette" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "56a25044-ea92-475a-91c9-101b20c7e5f6", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.14" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}