DOC-3222 RS: Clarified formula and examples for disk sizing for heavy write scenarios

Author: rrelledge

content/operate/rs/clusters/optimize/disk-sizing-heavy-write-scenarios.md

@@ -10,31 +10,127 @@ description: Sizing considerations for persistent disk space for heavy throughpu
 linktitle: Disk sizing
 weight: $weight
 ---
-In extreme write scenarios, when AOF is enabled, the AOF rewrite process
-may require considerably more disk space for database persistence.
-
-To estimate the required persistent disk space in such cases, use the
-formula described below.
-
-**The required persistent disk space for AOF rewrite purposes in extreme
-write scenarios, assuming identical shard sizes:**
-
-**X (1 + 3Y +Y²)**
-where:
-**X** = each shard size
-**Y** = number of shards
-
-Following are examples of database configurations and the persistence
-disk space they would require in this scenario:
-
-|   | Example 1 | Example 2 | Example 3 | Example 4 |
-|---|------------|-----------------|------------|-----------------|
-| Database size (GB) | 10 | 10 | 40 | 40 |
-| Number of shards | 4 | 16 | 5 | 15 |
-| Shard size (GB) | 2.5 | 0.625 | 8 | 2.67 |
-| Required disk space (GB) | 73 | 191 | 328 | 723 |
-
-For disk size requirements in standard usage scenarios, refer to the
-[Hardware
-requirements]({{< relref "/operate/rs/installing-upgrading/install/plan-deployment/hardware-requirements.md" >}})
-section.
+In extreme write scenarios when append-only files (AOF) are enabled, the AOF rewrite process can require considerably more disk space for [database persistence]({{<relref "/operate/rs/databases/configure/database-persistence/">}}).
+
+For disk size requirements for standard usage, see [Hardware requirements]({{< relref "/operate/rs/installing-upgrading/install/plan-deployment/hardware-requirements" >}}).
+
+## Estimate required disk space
+
+To estimate the required persistent disk space for AOF rewrite purposes in extreme write scenarios, use the following formula:
+
+**X (1 + 3Y + Y²)**
+
+Where:
+- **X** = size of each shard in GB
+- **Y** = number of shards
+
+
+## Examples
+
+The following examples show how to calculate the persistent disk space required for heavy write scenarios for different database configurations, where:
+
+- **Database size** is the memory limit configured for the database.
+
+- **Number of shards** is the total number of shards (primary shards + replica shards).
+
+### Example 1
+
+- Database size = 10 GB
+- Number of shards = 4
+
+1. Calculate the shard size:
+
+    ```sh
+    Shard size = database size / number of shards
+               = 10 GB / 4 shards
+               = 2.5 GB per shard
+    ```
+
+1. Use the formula to calculate the required persistent disk space:
+
+    ```sh
+    Disk space = X (1 + 3Y + Y²)
+               = 2.5 (1 + 3 × 4 + 4²)
+               = 2.5 (1 + 12 + 16)
+               = 2.5 × 29
+               = 72.5 GB
+    ```
+
+1. Round up to 73 GB of required disk space.
+
+### Example 2
+
+- Database size = 10 GB
+- Number of shards = 16
+
+1. Calculate the shard size:
+
+    ```sh
+    Shard size = database size / number of shards
+               = 10 GB / 16 shards
+               = 0.625 GB per shard
+    ```
+
+1. Use the formula to calculate the required persistent disk space:
+
+    ```sh
+    Disk space = X (1 + 3Y + Y²)
+               = 0.625 (1 + 3 × 16 + 16²)
+               = 0.625 (1 + 48 + 256)
+               = 0.625 × 305
+               = 190.625 GB
+    ```
+
+1. Round up to 191 GB of required disk space.
+
+### Example 3
+
+- Database size = 40 GB
+- Number of shards = 5
+
+1. Calculate the shard size:
+
+    ```sh
+    Shard size = database size / number of shards
+               = 40 GB / 5 shards
+               = 8 GB per shard
+    ```
+
+1. Use the formula to calculate the required persistent disk space:
+
+    ```sh
+    Disk space = X (1 + 3Y + Y²)
+               = 8 (1 + 3 × 5 + 5²)
+               = 8 (1 + 15 + 25)
+               = 8 × 41
+               = 328 GB
+    ```
+
+1. Required disk space: 328 GB.
+
+### Example 4
+
+- Database size = 40 GB
+- Number of shards = 15
+
+1. Calculate the shard size:
+
+    ```sh
+    Shard size = database size / number of shards
+               = 40 GB / 15 shards
+               = 2.67 GB per shard
+    ```
+
+1. Use the formula to calculate the required persistent disk space:
+
+    ```sh
+    Disk space = X (1 + 3Y + Y²)
+               = 2.67 (1 + 3 × 15 + 15²)
+               = 2.67 (1 + 45 + 225)
+               = 2.67 × 271
+               = 723.57 GB
+    ```
+
+1. Round up to 724 GB of required disk space.
+
+