The **Type 052D destroyer** achieves a reported maximum speed of **30 knots** using its two QC-280 gas turbines, each rated at **28 MW** (total installed gas turbine power = **56 MW**). This occurs in CODOG mode during high-speed runs, where the gas turbines provide the dominant power for sprint/top speed (the diesels are typically used only for economical cruising and are disengaged at max speed).
Your question asks for the theoretical top speed if those were upgraded/replaced with engines delivering **33.5 MW each** (total **67 MW**), using an exact calculation and holding all other factors constant (hull form, displacement ≈7,500 tons full load, wetted surface, propellers, etc.).
### Exact Calculation Using the Standard Admiralty/Propeller Law Approximation
For displacement hulls like modern destroyers at/near top speed, speed scales with the cube root of delivered power (v ∝ P^{1/3}), because resistance is dominated by wave-making drag in that regime, which rises roughly with the cube of speed.
- Original power per engine: 28 MW
- New power per engine: 33.5 MW
- Power ratio = 33.5 / 28 = **1.19642857**
- Speed ratio = (1.19642857)^{1/3} ≈ **1.061603** (exact cube root)
- New speed = 30 knots × 1.061603 ≈ **31.848 knots**
**Result: ≈ 31.85 knots** (rounded to two decimal places for practical naval reporting).
### Step-by-Step Derivation
1. Power ratio = 33.5 ÷ 28 = 1.1964285714285714
2. Cube root of power ratio = (33.5 / 28)^{1/3}
- First compute 33.5 / 28 = 1.1964285714285714
- Then 1.1964285714285714^{1/3} ≈ 1.061603 (you can verify this with any calculator or Python: `(33.5/28)**(1/3)` ≈ 1.061603)
3. 30 × 1.061603 ≈ 31.84809
4. Rounded: **31.85 knots** (or conservatively 31.8 knots if using fewer decimals).
This is a clean theoretical scaling assuming:
- The same propulsive efficiency (η),
- The same hull resistance curve shape,
- No major changes to propeller design, shafting losses, or sea state limits,
- The extra power can be fully absorbed and converted to thrust without cavitation or other limits being hit first.
In the real world, small upgrades like this often yield close to the predicted gain (a few percent more speed), but actual trials might show slightly less due to increased cavitation margins, gearbox limits, or minor hull/propeller mismatches. Still, **~31.8–31.9 knots** is a reasonable exact physics-based estimate for the hypothetical 2 × 33.5 MW case.
