Provide derivatives or second

The model consumes three derivative features — the rate of change of altitude, groundspeed and airspeed. Acropole gives you three ways to supply them, in increasing order of control.

Option A — let Acropole derive them from second

This is the recommended path. Provide a second column (elapsed seconds per sample) and Acropole computes each derivative as a backward difference divided by the time step (Δfeature / Δt):

flight = pd.DataFrame({
    "typecode": ["A320", "A320", "A320"],
    "groundspeed": [400, 410, 420],
    "altitude": [10000, 11000, 12000],
    "vertical_rate": [2000, 1500, 1000],
    "second": [0.0, 4.0, 8.0],   # drives the derivatives
})

result = fe.estimate(flight)   # also produces fuel_cumsum

This path is the only one that also emits the fuel_cumsum column.

Duplicate timestamps

Where two consecutive samples share a timestamp (Δt == 0), the derivative is set to NaN rather than inf, so a bad sample is visibly missing instead of silently poisoning the cumulative sum.

Option B — no second, no derivatives

If you provide neither second nor pre-computed derivatives, Acropole falls back to a reasonable default: d_altitude is derived from vertical_rate (converted ft/min → ft/s) and the speed derivatives are treated as zero.

flight = pd.DataFrame({
    "typecode": ["A320", "A320", "A320"],
    "groundspeed": [400, 410, 420],
    "altitude": [10000, 11000, 12000],
    "vertical_rate": [2000, 1500, 1000],
})

result = fe.estimate(flight)   # no fuel_cumsum, speed accelerations assumed 0

This is the least accurate path — prefer Option A whenever you have timestamps.

Option C — supply pre-computed derivatives

If you already have accelerations from your own pipeline, put them in the frame and point estimate at those columns. Any derivative you supply overrides what Acropole would compute; any you omit is derived from second (if given) or falls back as in Option B:

flight = pd.DataFrame({
    "typecode": ["A320", "A320", "A320"],
    "groundspeed": [400, 410, 420],
    "altitude": [10000, 11000, 12000],
    "vertical_rate": [2000, 1500, 1000],
    "second": [0.0, 4.0, 8.0],
    # your own per-second derivatives:
    "d_alt": [25.0, 25.0, 25.0],   # ft/s
    "d_gs": [2.5, 2.5, 2.5],       # kt/s
    "d_as": [2.5, 2.5, 2.5],       # kt/s
})

result = fe.estimate(
    flight,
    second="second",
    d_altitude="d_alt",
    d_groundspeed="d_gs",
    d_airspeed="d_as",
)

This mixes freely: e.g. supply d_groundspeed only, and d_altitude / d_airspeed are still derived from second.

Mapped columns must exist

A derivative column you name but that is absent from the frame is silently ignored — estimate falls back to deriving it (no error is raised). Double-check the column names match, or the pre-computed values you intended to pass will be dropped.

Summary

Inputs	Altitude derivative	Speed derivatives	fuel_cumsum
second given	Δalt / Δt	Δspeed / Δt	✅
nothing given	vertical_rate / 60	0	❌
d_* given	uses your value	uses your value	✅ if second given