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Follow the step-by-step instructions for CdA and Crr analysis

CdA Screenshots

How-to

FAQ

AeroStar CdA & Crr Analysis

AeroStar is a web-based app that runs in your browser. AeroStar reads Notio JSON and Garmin FIT files to calculate the cyclist's aerodynamic and rolling resistance using advanced mathematics.

AeroStar analysis is similar to energy-based Virtual Elevation, but instead of providing an average CdA value over a lap, AeroStar calculates the instantaneous CdA 4 times a second.

What other vendors show you what an ideal CdA ride and analysis looks like? The screenshots below show sub 0.001 CdA resolution.

What other vendors show you CdA & Crr confidence bounds and results that match analytical results? The graphs in Technology show excellent accuracy and precision.

AeroStar CdA & Crr is provably correct since it matches analytical solutions. Is AeroStar the world's most accurate CdA analysis tool? We think so.

CdA & Crr Solvers

AeroStar includes two separate solvers: M2 and M4.

Aerostar M2

Accurately calculate your CdA.
Uses Kalman Filters to compute your aero resistance.
Validate the CdA with Virtual Elevation. If the calculated CdA is accurate, then the calculated Virtual Elevation will match! If the VE is too high, then the CdA is too low (and vice versa).

Aerostar M4

Accurately calculate your CdA & Crr.
Uses Kalman Filters and LOTS more math tricks to simultaneously compute your aero and rolling resistance.
Compare your calculated Crr with the assumed rolling resistance, and update your Notio device.

Features & Benefits

Feature	Benefit
Web-app	An easy to use automated analysis environment. Runs in your desktop browser! No installation. Automatic updates.
Easy-to-use	Automated analyses -- no manual settings or slider adjustments. Simply load your ride, look at your CdA graph, and double-check the validation graphs!
High accuracy algorithms	Provably correct CdA & Crr when analyzing rides which have analytical results.
Kalman Filter estimates	AeroStar uses Kalman Filters (aka optimal observers) to estimate the unknown CdA & Crr parameters. With more data the estimates become more & more precise, and the accuracy is reported.
Kalman Filter replaces expensive sensors with math	Kalman Filters optimally combine a model of the dynamic system and (noisy) measurements. Often it is difficult or expensive or impossible to use sensors to accurately measure the system -- looking at you Body Rocket! -- instead Kalman Filters replace sensors with math!
Speed-independent algorithms	Stable and consistent CdA at any speed, even if you coast to a stop. In contrast the Notio CdA is speed-dependent resulting in huge swings.
Loads Notio files	Instant analysis using Notio sensor data. Some data (mass, Crr, density, elevation, airspeed) can be optionally modified.
Loads Garmin FIT files	Instant analysis using FIT power, groundspeed and elevation data. Other data (mass, Crr, density, airspeed) must be manually specified.
Map of the ride	A map shows the path of the ride. The starting and ending points are marked. Customizeable map type and zoom.
Graphs of primary sensor data	Quick sanity check -- do power, elevation, ground speed and airspeed all look good?
Graphs of any sensor or computed data	Zoom in and explore all the data available in your ride. Zoom to-fit or Zoom rectangle to look at detail.
Real-time CdA analysis	Kalman Filter-based analysis estimates real-time CdA (Notio 4Hz, FIT 1Hz) instead of a lap-average.
Updates Crr with persistent excitation	Advanced math updates the Crr estimate only when there is sufficient data (such as accelerating from low to high speed, or decelerating from high speed to low speed). No messing about trying to combine multiple rides into a Crr calculation!
Automatic CdA Validation	Computes the instantaneous Virtual Elevation, Virtual Power, Virtual Velocity and compares with the measured elevation, power and groundspeed. If they match then the AeroStar CdA is accurate. (Similarly you see that the Notio CdA is inaccurate.)
PDF Reports	Include any graph in a PDF report as ride summary.
Optional airspeed calibration	The calibration can be re-calculated from any ride.
Optional elevations	Measuring elevation is difficult with a noisy barometric altimeter. Lucky that Kalman Filter can reduce the noise. Or you can detrend the weather pressure using a high-pass filter. Or use a GPS-based Digital Elevation Model. Or specify a flat velodrome.

Sample CdA Analysis

Follow along as we use AeroStar to analyze a Notio file of a recreational rider.

AeroStar started. Press "Load" tab. Select Demo1 which is a simple 1 lap Out & Back ride. The checkmark shows that ride is loaded and analyzed.

Press "Map" tab to see path of ride. This is a fairly flat road adjacent the OAK airport. Not much traffic, but poor asphalt. There are no active turnoffs. There is a traffic light at the turn-around. Each leg is 1 mile (1.6km) long, so Out&Back is 2 miles.

Press "Sensors" tab to see major sensors.

Here we see that the elevation change is about 2m. For this first analysis we will use the elevation from the barometric altimeter. The "Options" menu has several alternative elevations.

The airspeed looks similar to the ground speed. The "Options" menu has several alternative airspeeds including recalibration.

Press "CdA&More" tab to see CdA (default view). Any sensor or computed value can be graphed on this page.

Position is hands-on-hoods with straight arms on a road bike. Note the "hump" at the turn-around on this Out&Back ride -- I sit up for more air resistance and coast to slow down trying to avoid the brakes -- so I expect the CdA to increase before & during the turn.

Zoomed in to CdA using zoom-rect icon in top-right. Note that Notio CdA is lower, and has a very pronounced "hump" at low-speed. Aerostar M2 CdA has much smaller variation than Notio CdA.

Later analyze Demo2 to see multiple laps of this Out&Back route. The Notio CdA has very large variations :(

Press "Validation" tab to see validation graphs of Aerostar M2. Excellent fit to virtual elevation (VE), so AeroStar M2 CdA is good.

Press radio buttons at top to select Notio. Note the poor fit of the validation graphs. Virtual Elevation (VE) refactors the energy balance

VE=(Ewheel-Eaero-Eroll-Eke)/(m*g)

If your Eaero is too low (ie CdA too low), VE thinks "Well your energy is going somewhere, so if it's not aero then you must be going up a hill!".

VE is too high = Notio CdA too low.

Re-run this analysis but use Demo2 (3 laps, Out&Back) to see that the Notio CdA (green) is extremely sensitive to velocity. The Notio CdA varies between 0.3-0.75 over each 1 mile leg. Argh! It was literally this ride that made me develop the AeroStar algorithms.

Repeat the CdA analysis yourself -- Right now!

Start AeroStar

Select Load>Demo1 and follow the steps in the screenshots.

Sample CdA & Crr Analysis

Follow along as we use AeroStar to analyze a Notio file of a competitive TT rider.

A consistent rider demonstrates sub 0.001 CdA change per lap!

AeroStar started. Press "Load" tab. Select Demo3 which is a test session at an outdoor velodrome. The checkmark shows that ride is loaded and analyzed.

Press "Map" tab to see path of ride.

Press "Sensors" tab to see major sensors. Note that the elevation shows a trend from the weather. This will adversely effect the analysis, so let's correct that.

Press "Load" tab again, then press the "Options" button to view a popup menu. Select "Velodrome" to set the elevation to zero.

Press "Sensors" again. Note that the elevation is now zero.

Press "CdA&More" tab to see the CdA (default view). Three curves are for Aerostar M4, Aerostar M2, and Notio CdA values.

Use the zoom-rect icon to zoom in. Yikes lots of variation here!

Hide all the graphs except Notio using the eye icons. Note that in the 5th set the Notio CdA has inter-lap changes of 0.010.

Hide all the graphs except Aerostar M2 using the eye icons. Higher CdA values. Once up to speed the AeroStar M2 CdA in the 5th set has inter-lap change of 0.005.

Hide all the graphs except Aerostar M4 using the eye icons. Wow this is qualitatively quite different -- M4 uses different algorithms than M2! Slightly lower CdA values (due to a slightly higher Crr), and tiny inter-lap variations.

Use the home icon to zoom-to-fit. There are 6 sets, each with 7 laps. The CdA variation between all 42 laps is about 0.006.

Use the crosshair icon to see the CdA in the 5th set.

Use the zoom-rect to zoom into the 5th set.

Wow the graph is showing us sub 0.001 CdA resolution! In the 5th set the CdA variation between the 7 laps is about 0.0015. That is only 1.2W at 11 m/s.

This competitive rider is well known for his low CdA -- now you see his consistency!

Let's now look at the Crr. Press the button on the top-left to show a popup menu of data. Select Crr.

The AeroStar M4 computed Crr is about 0.0043. If you use the "Options" menu to adjust the Crr setting from 0.0040 to 0.0043 then the M2 and M4 curves will match up nicely.

Note that M4 algorithms only try to adapt the CdA and Crr when there is sufficient excitation for accurate parameter excitation. Here you see that the Crr changes with transitions from slow speed to high speed.

There are ~100 data sources available to graph. Explore a little! Here we see the popup menu for the environmental sensors.

Press "Report" tab. Let's create a report for the ride and analyses. Whoops it's empty! We forgot to use the camera icon to add graphs to our report. OK go back and add some interesting graphs...

Now we have some report items. You can edit them by clicking. Delete by swiping. Rearrange by clicking the up/down buttons. Let's edit the CdA item.

Annotate using HTML formatting.

Now we have several annotated graphs in the order we want to present them. Press the PDF icon at the top-right to generate a PDF file.

And here's the PDF report ready to send to the rider. The first pages contain details of the Notio device settings, then there is a page for each report item. Well Done!

This ride was actually an ABABAB test of two aero helmets. Excellent data let AeroStar M4 show us instantaneous CdA with sub 0.001 resolution. Based on your analysis, which helmet do you recommend and why?

Repeat the CdA & Crr analysis yourself -- Right now!

Start AeroStar

Select Load>Demo3 and follow the steps in the screenshots.

Products

AeroStar CdA & Crr Analysis

CdA & Crr Solvers

Aerostar M2

Aerostar M4

Features & Benefits

Feature

Benefit

Web-app

An easy to use automated analysis environment. Runs in your desktop browser! No installation. Automatic updates.

Easy-to-use

Automated analyses -- no manual settings or slider adjustments. Simply load your ride, look at your CdA graph, and double-check the validation graphs!

High accuracy algorithms

Provably correct CdA & Crr when analyzing rides which have analytical results.

Kalman Filter estimates

AeroStar uses Kalman Filters (aka optimal observers) to estimate the unknown CdA & Crr parameters. With more data the estimates become more & more precise, and the accuracy is reported.

Kalman Filter replaces expensive sensors with math

Kalman Filters optimally combine a model of the dynamic system and (noisy) measurements. Often it is difficult or expensive or impossible to use sensors to accurately measure the system -- looking at you Body Rocket! -- instead Kalman Filters replace sensors with math!

Speed-independent algorithms

Stable and consistent CdA at any speed, even if you coast to a stop. In contrast the Notio CdA is speed-dependent resulting in huge swings.

Loads Notio files

Instant analysis using Notio sensor data. Some data (mass, Crr, density, elevation, airspeed) can be optionally modified.

Loads Garmin FIT files

Instant analysis using FIT power, groundspeed and elevation data. Other data (mass, Crr, density, airspeed) must be manually specified.

Map of the ride

A map shows the path of the ride. The starting and ending points are marked. Customizeable map type and zoom.

Graphs of primary sensor data

Quick sanity check -- do power, elevation, ground speed and airspeed all look good?

Graphs of any sensor or computed data

Zoom in and explore all the data available in your ride. Zoom to-fit or Zoom rectangle to look at detail.

Real-time CdA analysis

Kalman Filter-based analysis estimates real-time CdA (Notio 4Hz, FIT 1Hz) instead of a lap-average.

Updates Crr with persistent excitation

Advanced math updates the Crr estimate only when there is sufficient data (such as accelerating from low to high speed, or decelerating from high speed to low speed). No messing about trying to combine multiple rides into a Crr calculation!

Automatic CdA Validation

Computes the instantaneous Virtual Elevation, Virtual Power, Virtual Velocity and compares with the measured elevation, power and groundspeed. If they match then the AeroStar CdA is accurate. (Similarly you see that the Notio CdA is inaccurate.)

PDF Reports

Include any graph in a PDF report as ride summary.

Optional airspeed calibration

The calibration can be re-calculated from any ride.