Air-dropped accelerometer probe for snow stratigraphy and characterization

Abstract

Current measurements for avalanche forecasting are usually taken by digging snow pits or probing. These methods are mostly either fast and qualitative or slow and quantitative. The method disclosed herein offers an approach that is both fast and quantitative and could be useful to backcountry skiers and ski patrollers. The air-dropped system disclosed herein would also be useful for characterizing snow water content, which is useful for estimating city water supplies, particularly in draught-stricken places. Existing ways of measuring sown water content involve taking precise density measurements in particular locations, but these air-dropped techniques could be performed over a much wider area to get a better idea of the distribution of the water content, leading to better estimates of city water supply.

Description

[0001] AIR-DROPPED ACCELEROMETER PROBE FOR SNOW STRATIGRAPHY AND CHARACTERIZATION

[0002] RELATED APPLICATIONS

[0003] This application claims the benefit of US Provisional Application No. 63 / 557,022, filed 23 February 2024, and the benefit of US Provisional Application No. 63 / 557,471, filed 23 February 2024, the entire contents of each of which is incorporated herein by reference.

[0004] GOVERNMENT SUPPORT

[0005] This invention was made with US government support under Grant No. 1931131 awarded by the National Science Foundation. The US government has certain rights in the invention.

[0006] BACKGROUND

[0007] The discussion of the background state of the art below may reflect hindsight gained from the disclosed invention(s), and these characterizations are not necessarily admitted to be prior art.

[0008] Current measurements for avalanche forecasting are usually taken by digging snow pits or probing. These methods are mostly either fast and qualitative or slow and quantitative. There is a need for a method that offers an approach that is both fast and quantitative, and could be useful to backcountry skiers and ski patrollers.

[0009] This air-dropped system would also be useful for characterizing snow water content, which is useful for estimating city water supplies in mountainous regions, such as the Sierra Nevada, the Rockies, or the Alps. Existing ways of measuring snow water content involve taking precise density measurements in particular locations.

[0010] SUMMARY

[0011] This Summary introduces a selection of concepts in simplified form that are described further below in the Detailed Description. This Summary neither identifies key or essential features, nor limits the scope, of the claimed subject matter.

[0012] A drop probe system includes a drop probe including a nose at one end and a tail at an opposite end of an elongated body. The drop probe further includes a power source contained in the elongated body; a computing device including a processor and a timing device and in electrical communication with the power source; an on-board accelerometer in communication with the computing device; a global positioning system in communication with the computing device; a motion sensor in communication with the computing device; a thermocouple in communication with the computing device; a weighted mass positioned proximate to the nose to place a center of gravity of the drop probe closer to the nose than a center of pressure of the drop probe, as measured when the drop probe orthogonally penetrates a bed of snow with the nose leading; and an attachment mechanism at the tail for attachment to cordage.

[0013] A method of using this drop probe system includes implanting the drop probe into surface snow on a mountain and transmitting data relating to properties of the surface snow. The drop probe can be implanted by dropping the drop probe (e.g., from a drone) into the surface snow.

[0014] A computer system for calculating (measuring) the water content of surface snow on a mountain includes a processor and a timing device; computer memory storage accessible to the processor, and computer program instructions encoded in the computer memory storage. When the computer program instructions are processed by the processing system, the computer system is configured to define data structures in the computer memory storage representing data from the drop probe system; and to execute algorithms of Equations (2) to (19), presented in the Detailed Description, applied to the data structures to calculate the water content of surface snow in which the drop probe is dropped on a mountain.

[0015] A computer program product including computer memory storage and computer program instructions encoded in the computer memory storage, wherein the computer program instructions, when processed by a processor of a computer, causes the computer to determine the mass of the surface snow from the above method.

[0016] The air-dropped techniques described herein can be performed over a much wider area than previous approaches to get a better idea of the distribution of the water content, leading to better estimates of city water supply.

[0017] The following Detailed Description references the accompanying drawings which form a part of this application, and which show, by way of illustration, specific example implementations. Other implementations maybe made without departing from the scope of the disclosure.

[0018] BRIEF DESCRIPTION OF THE DRAWINGS

[0019] FIG. 1 is a side view of the disclosed probe 10 and its chief functional components.

[0020] FIG. 2 is a top view of the disclosed probe and 10 its chief functional components.

[0021] FIG. 3 shows the probe 10 attached to a drone or unmanned aerial vehicle 12 for transporting to a site of interest.

[0022] FIG. 4 shows the probe 10 for hand delivery to a site of interest.

[0023] FIG. 5 shows the probe 12 in a cannon device 14 for delivery to a site of interest. FIG. 6 schematically shows an example of a computer 500 that comprises a processing system, including at least one processing unit 502 and a memory storage device 504.

[0024] FIG. 7 shows a compaction model that features an infinite grid of 1D elastic elements 16 with modulus, E, that depends nonlinearly on the material density.

[0025] FIG. 8 schematically shows a microcontroller circuit board 20, including an electronic microcontroller 50, including an accelerometer 52, a global positioning system (GPS) module 54, and a battery management system 56. The microcontroller circuit board 20 is further coupled with and in communication with computer memory storage 58.

[0026] In the accompanying drawings, like reference characters refer to the same or similar parts throughout the different views. The drawings are not necessarily to scale; instead, an emphasis is placed on illustrating particular principles in the exemplifications discussed below. For any drawings that include text (words, reference characters, and / or numbers), alternative versions of the drawings without the text are to be understood as being part of this disclosure; and formal replacement drawings without such text may be substituted therefor.

[0027] DETAILED DESCRIPTION

[0028] The foregoing and other features and advantages of various aspects of the invention(s) will be apparent from the following more particular description of various concepts and specific implementations within the broader bounds of the invention(s). Various aspects of the subject matter introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the subject matter is not limited to any particular manner of implementation. Examples of specific implementations and applications are provided primarily for illustrative purposes.

[0029] Unless otherwise herein defined, used, or characterized, terms that are used herein (including technical and scientific terms) are to be interpreted as having a meaning that is consistent with their accepted meaning in the context of the relevant art and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein. For example, if a particular composition is referenced, the composition may be substantially (though not perfectly) pure, as practical and imperfect realities may apply; e.g., the potential presence of at least trace impurities (e.g., at less than 1 or 2%) can be understood as being within the scope of the description. Likewise, if a particular shape is referenced, the shape is intended to include imperfect variations from ideal shapes, e.g., due to manufacturing tolerances. Percentages or concentrations expressed herein can be in terms of weight or volume. Processes, procedures, and phenomena described below can occur at ambient pressure (e.g., about 50-120 kPa— for example, about 90-110 kPa) and temperature (e.g., -30 to io°C unless otherwise specified.

[0030] Although the terms, first, second, third, etc., maybe used herein to describe various elements, these elements are not to be limited by these terms. These terms are simply used to distinguish one element from another. Thus, a first element, discussed below, could be termed a second element without departing from the teachings of the exemplary implementations.

[0031] Spatially relative terms, such as “above,” “below,” “left,” “right,” “in front,” and “behind,” may be used herein for ease of description to describe the relationship of one element to another element, as illustrated in the figures. It will be understood that the spatially relative terms, as well as the illustrated configurations, are intended to encompass different orientations of the apparatus in use or operation in addition to the orientations described herein and depicted in the figures. For example, if the apparatus in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term “above” may encompass both an orientation of above and below. The apparatus may be otherwise oriented e.g., rotated 90 degrees or at other orientations), and the spatially relative descriptors used herein should be interpreted accordingly. The term “about” can mean within ± 10% of the value recited. In addition, where a range of values is provided, each subrange and each individual value between the upper and lower ends of the range is contemplated and, therefore, disclosed.

[0032] Further still, in this disclosure, when an element is referred to as being “on,” “connected to,” “coupled to,” “in contact with,” etc., another element, it may be directly on, connected to, coupled to, or in contact with the other element or intervening elements may be present unless otherwise specified.

[0033] Some of the terminology used herein is associated with particular implementations and is not intended to limit more generic exemplifications of the invention. As used herein, singular forms, such as those introduced with the articles, “a” and “an,” are intended to include the plural forms as well, unless the context indicates otherwise. Additionally, the terms “includes,” “including,” “comprises,” and “comprising” specify the presence of the stated elements or steps but do not preclude the presence or addition of one or more other elements or steps.

[0034] Additionally, the various components identified herein can be provided in an assembled and finished form; or some or all of the components can be packaged together and marketed as a kit with instructions (e.g., in written, video, or audio form) for assembly and / or modification by a customer to produce a finished product. Disclosed herein is a small, air-dropped metal probe 10 (around 0.3-m long with a mass of 2 kg), as shown in FIGS. 1 and 2, that can be dropped into snow to characterize the stratigraphy of the snow. The probe 10 has a well-characterized tip shape (can be pointy or rounded), with, e.g., a cone end 18, that is known to go into snow of different elastic moduli with different accelerations. The probe has an accelerometer (e.g., as a component of a microcontroller circuit board 20) inside that can record the acceleration values during the impact, and it runs an algorithm that translates the acceleration readings to a stratigraphy profile.

[0035] Electronics:

[0036] The probe comprises an electronic microcontroller 50 as a key component of the microcontroller circuit board 20, which is also schematically illustrated in FIG. 8. The microcontroller 50 collects data from sensors and initiates processing of the data. The microcontroller 50 can display the data on a display screen 22 (shown in FIG. 2) or can transmit the data to a remote site (e.g., via either a Bluetooth transmission to a cell phone or a radio transmission to a remote receiver, such as a drone, satellite, or nearby radio tower).

[0037] The probe 10 may include the following components:

[0038] • a mini-LCD or OLED screen 22 that shows a simple representation of collected data and system state.

[0039] • an accelerometer 52 (e.g., a 200-g, three-axis accelerometer as a component of the microcontroller circuit board 20), which is the main sensor for data collection;

[0040] • an optical motion sensor 24 used to add additional context to data;

[0041] • a GPS module 54, which can be included as a component of the microcontroller circuit board 20 and in communication with the microcontroller, to timestamp and localize data;

[0042] • a temperature sensor 26 (e.g., including a thermocouple) that reads temperature near the tip for rapid response;

[0043] • a memory (e.g., SD card) reader / writer or other form of computer memory storage 58 in communication with the microcontroller;

[0044] • a charging and / or data-transfer port 27 in communication with the microntroller;

[0045] • a small battery 28 coupled with and configured for powering the microcontroller, sensors, and transmitter / receiver;

[0046] • a battery management system 56 coupled with the microcontroller 50 and the battery 28 to control charging and discharging of the battery 28; and • one or more control buttons 29 for turning the device on / off, changing its mode of operation, and / or changing the data displayed.

[0047] Mechanical:

[0048] The device comprises a small, air-dropped metal probe 10 (around 0.3 m long, 2 kg). The probe 10 can include a steel outer casing 30. The back (top) portion of the casing 30 is secured with screws 31 such that the electronics may be removed. The probe 10 further comprises a hook 32 or other attachment mechanism coupled via a hook fitting 36 on the back portion for use in transport.

[0049] The front (bottom) section of the probe e.g., in the form of a cone end 18) can be filled with lead or another heavy (dense) substance 34 (z.e., with higher density than the rest of the probe) to add stability.

[0050] For deployment, a spool 38, as shown in FIG. 4, can be used to unfurl cordage (a line), such as rope, cord, or metallic or plastic cable. The spool can have a relatively low- friction brake that adds stability to the drop probe, as well as a pin-puller release mechanism for dropping the probe. Additionally, the spool can be coupled with a motor to form a winch so that the probe may be automatically retrieved.

[0051] Deployment:

[0052] The probe and the probe system are deployed via at least one of the following methods.

[0053] First, the probe 10 can be dropped by hand on, e.g., a snow slope 39, as shown in FIG. 4. A spool 38 of small cordage 40 e.g., rope) can be held in a human hand with a low friction brake and a release mechanism that delivers a cleaner drop and level release. To recover the probe 10 from the snow, the person lifts the spool 38 to pull out the attached probe 10.

[0054] Second, a similar spool 38 and motorized winch system with a brake and release mechanism can be mounted on a drone 12, as shown in FIG. 3. The drone 12 can be used to drop the probe 10 for automated snow stratigraphy mapping over a very large area.

[0055] Third, the probe 10 can be dropped from a tower, such as a chairlift tower. The tower can have a spool at the top that can rapidly release cordage and can be actuated like a winch to retrieve the system from the snow. The spool can be rotated or translated around the tower to change the exact location where the drop probe lands. This technique can be used to measure compaction of the same snowpack over time or to take numerous repeated measurements.

[0056] Fourth, the probe 10 can be launched out of an air cannon 14 powered by a pressurized air tank 42 with the pressurized air delivered from the tank 42 through a hose 44 to the cannon 14 while subject to controlled release by a large butterfly valve 46, as shown in FIG. 5. The air cannon 14 can also contain packing material 48 upstream from the probe 10 so as not to inhibit launch of the probe 10 from the cannon 14. The air cannon 14 can be useful to assess far-away snowpacks in areas where drone use is not permitted. Additionally, the air cannon 14 can be used to get higher probe velocity when deeper probing is needed.

[0057] Data processing / software:

[0058] The system comprises a computer memory device storing an algorithm that translates acceleration to snow density using a nonlinear elastic compression method comprising localizing the drop probe by using the GPS and determining the GPS time for logging. When the acceleration is above a threshold e.g., 10 g), the previous 30 seconds of data and the following 5 seconds from the accelerometer and motion sensor are recorded to the onboard SD card. That data is processed by detecting the time of the drop release based on the drop in accelerometer value to freefall condition and noting the timestamp, detecting the time of the initial impact and note the timestamp. Based on these timestamps and the aerodynamic parameters, the impact velocity and initial kinetic energy are estimated.

[0059] The initial kinetic energy and the acceleration profile (from the accelerometer and optical motion sensor) are used to calculate the snow stratigraphy, and the processed data is saved to the SD card with timestamps. The stratigraphy profile is displayed on the onboard display; and, if a cell phone is connected computer, both the raw data and the processed data are transferred via a wireless (e.g., Bluetooth) communication, and the data is displayed in a configurable graphic view. The application (app) can store profiles from several users for many locations and display the locations on a map. The app is configured to take the raw data and reprocess it with additional information inputs. These inputs include:

[0060] • a measured drop height from a laser altimeter (if dropped from a drone), or by hand measurement, yielding a more accurate initial velocity estimate; and

[0061] • data frames from temperature-sensing satellites for the snow season to estimate where ice layers are in the snowpack;

[0062] The app can automatically spatially average between profiles taken nearby within a short time window.

[0063] Computer:

[0064] One or more computers can be used to implement such a computational pipeline, using one or more general-purpose computers, such as client devices, including mobile devices and client computers, one or more server computers, or one or more database computers, or combinations of any two or more of these, which can be programmed to implement the functionality, such as is described in the example implementations.

[0065] FIG. 6 is a block diagram of a general-purpose computer that processes computer programs using a processing system. Computer programs on a general- purpose computer generally include an operating system and applications. The operating system is a computer program running via a processor in the computer that manages access to resources of the computer by the applications and the operating system. The resources generally include memory, storage, communication interfaces, input devices, and output devices.

[0066] Examples of such general -purpose computers include, but are not limited to, larger computer systems, such as server computers, database computers, desktop computers, laptop, and notebook computers, as well as mobile or handheld computing devices, such as a tablet computer, handheld computer, smart phone, media player, personal data assistant, audio and / or video recorder, or wearable computing device.

[0067] With reference to FIG. 6, an exemplary computer 500 comprises a processing system including at least one processing unit 502 and a memory 504. The processing unit 502 can include or can be in communication with a timing device, such as a crystal oscillator, to provide a stable clock signal for digital integrated circuits to track received information as a function of time. The computer can have multiple processing units 502 and multiple devices implementing the memory 504. A processing unit 502 can include one or more processing cores (not shown) that operate independently of each other. Additional co-processing units, such as a graphics processing unit 520, also can be present in the computer. The memory storage device 504 may include volatile devices (such as dynamic random-access memory (DRAM) or other random-access memory device) and non-volatile devices (such as a read-only memory, flash memory, and the like) or some combination of the two, and may optionally include any memory available in a processing device. Other memory, such as dedicated memory or registers, also can reside in a processing unit. Such a memory configuration is delineated by the dashed line 504 in FIG. 6. The computer 500 may include additional storage (removable and / or non-removable) including, but not limited to, solid-state devices or magnetically recorded or optically recorded disks or tape. Such additional storage is illustrated in FIG. 6 by removable storage 508 and non-removable storage 510. The various components in FIG. 6 are generally interconnected by an interconnection mechanism, such as one or more buses 530.

[0068] A computer memory storage medium is any medium in which data can be stored in and retrieved from addressable physical storage locations by the computer. Computer memory storage media includes volatile and nonvolatile memory devices and removable and non-removable storage devices. Memory 504, removable storage 508, and non-removable storage 510 are all examples of computer memory storage media. Some examples of computer memory storage media are RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optically or magneto-optically recorded storage device, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices. Computer memory storage media and communication media are mutually exclusive categories of media.

[0069] The computer 500 may also include communications connection(s) 512 that allow the computer to communicate with other devices over a communication medium. Communication media typically transmit computer program code, data structures, program modules, or other data over a wired or wireless substance by propagating a modulated data signal, such as a carrier wave or other transport mechanism, over the substance. The term "modulated data signal" means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal, thereby changing the configuration or state of the receiving device of the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct -wired connection, and wireless media include any non-wired communication media that allows propagation of signals, such as acoustic, electromagnetic, electrical, optical, infrared, radio frequency and other signals. Communications connections 512 are devices, such as a network interface or radio transmitter, that interface with the communication media to transmit data over and receive data from signals propagated through communication media.

[0070] The communications connections can include one or more radio transmitters for telephonic communications over cellular telephone networks and / or a wireless communication interface for wireless connection to a computer network. For example, a cellular connection, a Wi-Fi connection, a Bluetooth connection, and other connections may be present in the computer. Such connections support communication with other devices, such as to support voice or data communications.

[0071] The computer 500 may have various input device(s) 514 such as any of various pointer (whether single pointer or multi-pointer) devices, such as a mouse, tablet and pen, touchpad and other touch-based input devices, stylus, image input devices, such as still and motion cameras, audio input devices, such as a microphone. The computer may have various output device(s) 516, such as a display, speakers, printers, and so on, any of which also may be included.

[0072] The various storage 510, communication connections 512, output devices 516, and input devices 514 can be integrated within a housing of the computer or can be connected through various input / output interface devices on the computer, in which case the reference numbers 510, 512, 514 and 516 can indicate either the interface for connection to a device or the device itself as the case may be.

[0073] An operating system of the computer typically includes computer programs, commonly called drivers, which manage access to the various storage 510, communication connections 512, output devices 516, and input devices 514. Such access generally includes managing inputs from and outputs to these devices. In the case of communication connections, the operating system may also include one or more computer programs for implementing communication protocols used to communicate information between computers and devices through the communication connections 512.

[0074] Any of the foregoing aspects may be embodied as a computer system, as any individual component of such a computer system, as a process performed by such a computer system or any individual component of such a computer system, or as an article of manufacture, including computer memory storage in which computer program code is stored and which, when processed by the processing system(s) of one or more computers, configures the processing system(s) of the one or more computers to provide such a computer system or individual component of such a computer system.

[0075] Each component, which also may be called a “module” or “engine” or “computational model” or the like, of a computer system, such as described herein, and which operates on one or more computers, can be implemented as computer program code processed by the processing system(s) of one or more computers. Computer program code includes computer-executable instructions and / or computer-interpreted instructions, such as program modules, that are processed by a processing system of a computer. Generally, such instructions define routines, programs, objects, components, data structures, etc., that, when processed by a processing system, instruct the processing system to perform operations on data or configure the processor or computer to implement various components or data structures in computer memory storage. A data structure is defined in a computer program and specifies how data is organized in computer memory storage, such as in a memory device or a storage device, so that the data can accessed, manipulated, and stored by a processing system of a computer.

[0076] Data Analysis:

[0077] Compaction Model:

[0078] The simplest model of penetration is the Young model, which calculates penetration depth, z, as follows: where S is a dimensionless factor to denote the penetrability of the target material; N is a dimensionless nose performance coefficient. For conic nose shapes, this is given as N = + 0.56, where Lnis the length of the nose, and dn is the diameter of the nose.

[0079] 4d„ m [kg] is the mass of the probe; A [m2] is the frontal area of the probe; and v [ms1] is the impact velocity of the probe.

[0080] While the Young model presents a simple 1D phenomenology of impact mechanics, useful design decision making requires a more full-featured model that can directly correlate to measurable snow material properties. Thus, a nonlinear compaction model is presented that predicts a full impact trajectory based on the impact material elastic modulus, speed of sound, and impactor initial velocity and dimensions.

[0081] The nonlinear elastic compaction model uses a set of elastic "spring" elements that are arranged radially around the site of impact, such as shown in FIG. 7. During impact, these elements deform radially, with the nose cone forcing these elements outwards; it is assumed in this model that there is no vertical transport of material. The model splits the impact material into discrete and non-interacting radial slices; each slice has a known volumetric change from the probe going through the target material. Although the slices are shaped like an annulus, the compaction is solved as a set of 1D problems arranged radially. Since the elastic modulus is highly nonlinear with strain, the energy absorption in a volumetric element is calculated by a series of infinitesimal elastic deformations, each at a different strain and corresponding elastic modulus. By adding up all of the compacting elements, the amount of energy absorbed in each vertical layer slice may be calculated and used to form a complete impact trajectory.

[0082] Assumptions and Justification:

[0083] This nonlinear compaction model makes the following assumptions, each of which has the following implications on model applicability.

[0084] All energy absorbed during impact is absorbed through compaction. This model neglects other energy absorption modalities in snow, such as frictional interaction during particle transport and fracture. Thus, this model is most applicable to surface snow with densities below 600 kg m-3 and no significant crust or ice lens features. For impact materials with fracturing features at the surface, this model may be superimposed with another model on a layer-by-layer basis.

[0085] All is absorbed in the radial direction. Since this system is modeled as an infinite network of compressive elements that only compress in the radial direction, it is implied that there is no vertical transport of snow during impact. This assumption is close to valid for nose-cone shapes with — — — > 1 with an ideal ratio being force- body significantly higher; that is, pointier nose geometries are a better at transporting material radially rather than vertically. In most impacts, there is an area of newly compressed material directly in front of and to the side of the probe; the ratio of these depends on the total depth of penetration. Thus, this elastic compaction model is most valid for impacts that reach a depth of |z| > 6rforce-body.

[0086] The impact is nonlinear and elastic. This model models inelastic energy by iteratively evaluating small elastic deformations of individual material elements with an elastic modulus that is nonlinear with respect to the strain without consideration of strain rate. In reality, the deformations are inelastic and strain-rate dependent.

[0087] Mathematical Overview and Model Inputs:

[0088] In an elastic deformation of snow, the elastic modulus is given by a power law shown in Equation (2) this forms a nonlinearity where the material becomes stiffer the more it has been compacted. In this model, the elastic modulus is used rather than the bulk modulus, E, because the compression is uniaxial and shear is neglected. The elastic modulus can be calculated as follows:

[0089] E = cpk[Pa], (2) where p [kg m~3] is the density of snow; c is a non-dimensional fitting constant, derived through material testing; and k is a non-dimensional fitting constant, derived through material testing.

[0090] The nonlinear elastic model considers deformations in uniaxial strain, c. depicted in Equation (3) as follows: where I [m] is the deformed length of a cube of material along the radial axis of the probe, and Iceii [m] is the original undeformed length of a cube of material.

[0091] In a generalized cube of impact media, a strain is applied that changes the density of the impact media. The relation between strain and density, p, is expressed in Equation (4), as follows:

[0092] [kg m-3], (4) where mceii [kg] is the mass of the cube under consideration, which is invariant through deformation, and is calculated using the starting density and volume. During a generalized uniaxial compaction of a cube of material from an initial density to a final density, the final strain, £ / , is calculated in Equation (5). where p0[kg m~3] is the density of the cube of snow before compaction, and pf [kg m~3] is the density of the cube of snow after compaction.

[0093] From Equation (3), the initial strain, £0, before any compaction occurs in each cube of impact material is given in Equation (6), as follows: so= O [ ]. (6)

[0094] In a compaction event with a defined starting and ending strain, the change in volume, dVceii, in a cube is shown in Equation (7), as follows:

[0095] In a simple 1D compaction of a cube, the energy stored in that cube, Uceii, is given in Equation (8). Note that the elastic modulus is depicted as a function of density, which is a function of strain, the variable of integration.

[0096] By plugging in Equation (2). this expression yields Equation (9).

[0097] An advantage of using a power law fit for the elastic modulus nonlinearity is that this expression may be solved analytically, enormously speeding up computation times compared to a numerical integration procedure. This new expression is shown in Equati

[0098] In the oversimplified case where all cubic cells within the same layer, z, are compacted to the same final strain, the total energy per layer, uiayer, may be written simply in Equation (11). This is an oversimplification that will be explored and amended later but is useful conceptually and for making faster runtime solvers. By totaling up the energy absorbed in all layers through this procedure, the complete impact mechanical trajectory may be simulated.

[0099] Final Compacted Condition:

[0100] In the simplest formulation of the nonlinear compaction model, a simplification is made, which implies that all cells in each vertical layer are compacted to the same final strain and the corresponding final density. This is clearly an oversimplification because material further away from the probe should be compacted less than material directly next to the probe. In many cases, such as in quick design studies, this maybe an appropriate simplification because it leads to much faster runtimes. However, a significant issue is that it leaves a free parameter for pf or £ / , the final compacted condition. Fortunately, this parameter maybe evaluated experimentally if needed to validate models, unlike the free S parameter in the Young model. Nevertheless, it is valuable to see what bounds exist on this final compacted condition and to find a value of £ (r), which depends on r.

[0101] Due to the nature of uniaxial compression occurring in the nose-cone region of the impactor, an upper bound of the furthest away compacted element on each z may be found using the speed of sound in the impact medium. This is calculated in Equation (12). where leone [m] is the length of the nose cone of the probe,. vSOund [m s-1] is the speed of sound in snow, and Vpenetrator [m s-1] is the velocity of the probe evaluated at the height z of the layer of interest.

[0102] If it is assumed that the number of elements compacted is dictated by the speed of sound, across the elements in a layer affected during the compaction event, the average final strain, sf, between all of the elements is expressed in Equation (13). However, since the elastic modulus is nonlinear in strain, it is valuable to solve for the specific strain at each radius value. In reality, Ef is a lower bound, since there might be factors in compression that prevent compaction all the way to rS0Und, such as granular interactions between snow grains. The corresponding lower bound average density across all compacted elements in a layer is given in Equation (14).

[0103] Because the nonlinear elastic model detailed here is in spherical coordinates, decay of strain is expected to roughly follow a rate of — , adjusted with some constants. r

[0104] Thus, the form of £f (r) is expected to follow that of the “Compaction Model” section, above. where a is a non-dimensional fitting constant, and b << 1 is a non-dimensional fitting constant to prevent divide-by-zero issues.

[0105] Using the general expression for the average value of a function, the average value of E / (r) can be used to solve for a. This is shown in Equation (16) and Equation (17), as follows:

[0106] Plugging the value of a from Equation (17) and the value of ey from Equation (14) into an expression for the final strain in each element as a function of r, £r, is described in Equation (18).

[0107] Incorporating this final compaction condition, the energy absorbed in a cubic cell, ucrf / |r, under nonlinear elastic compaction is given in Equation (19). This modified expression can replace Equation (10) in the same procedure where the compacted cells in each layer are added up, and then, using all of the layers, the system is integrated to yield an impactor trajectory. Equations 2 through 19 are applied to data in the forward direction for a wide variety of input density values; then, to get the inverse, those calculated values are interpolated using the “measured” acceleration, and the calculated position and velocity using the accelerometer data (and optical motion sensor if there is one). A lookup table can be stored on the device where these values have been precomputed. The “final compacted condition” equations may be applied to form a bound.

[0108] In describing implementations herein, specific terminology is used for the sake of clarity. For the purpose of description, specific terms are intended to at least include technical and functional equivalents that operate in a similar manner to accomplish a similar result. Additionally, in some instances where a particular implementation includes a plurality of system elements or method steps, those elements or steps may be replaced with a single element or step. Likewise, a single element or step may be replaced with a plurality of elements or steps that serve the same purpose. Further, where parameters for various properties or other values are specified herein for implementations, those parameters or values can be adjusted up or down by 1 / 100*, 1 / 50*, 1 / 20*, i / ioLh, 1 / 5*, i / 3rd, 1 / 2, 2 / 3rd, 3 / 4*, 4 / 5111, 9 / ioth, 19 / 20*, 49 / 50*, 99 / 100*, etc. (or up by a factor of 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, etc.), or by rounded- off approximations thereof or within a range of the specified parameter up to or down to any of the variations specified above (e.g., for a specified parameter of 100 and a variation of 1 / 100th, the value of the parameter may be in a range from 0.99 to 1.01), unless otherwise specified. Further still, where methods are recited and where steps / stages are recited in a particular order— with or without sequenced prefacing characters added for ease of reference— the steps / stages are not to be interpreted as being temporally limited to the order in which they are recited unless otherwise specified or implied by the terms and phrasing.

[0109] Additional examples consistent with the present teachings are set out in the following numbered clauses:

[0110] 1. A drop probe system including a drop probe including a nose at one end and a tail at an opposite end of an elongated body, the drop probe comprising: a power source contained in the elongated body; a computing device including a processor and a timing device and in electrical communication with the power source; an on-board accelerometer in communication with the computing device; a global positioning system in communication with the computing device; a motion sensor in communication with the computing device; a thermocouple in communication with the computing device; a weighted mass positioned proximate to the nose to place a center of gravity of the drop probe closer to the nose than a center of pressure of the drop probe, as measured when the drop probe orthogonally penetrates a bed of snow with the nose leading; and an attachment mechanism at the tail for attachment to cordage.

[0111] 2. The drop probe system of clause 1, wherein the drop probe is less than about 30 cm long from nose to tail and has a mass of less than about 2 kg.

[0112] 3. The drop probe system of clause 1, wherein the motion sensor is an optical motion sensor.

[0113] 4. The drop probe system of clause 1, wherein the attachment mechanism is a hook.

[0114] 5. The drop probe system of clause 1, further comprising a display screen in communication with the computing device and configured to display data based on measurements from at least one of the accelerometer, the global positioning system, the motion sensor, or the thermocouple.

[0115] 6. The drop probe system of clause 1, further comprising an unmanned aerial vehicle (UAV), wherein the drop probe is attached to the UAV by a motorized winch comprising a brake and release mechanism.

[0116] 7. The drop probe system of clause 1, further comprising a spool configured for hand dropping the drop probe, wherein the drop probe is configured for entry into snow on a slope.

[0117] 8. The drop probe system of clause 1, further comprising a cannon configured for propelling the drop probe more than 10 meters, wherein the cannon comprises: a tube with packing material at its base; a hose connecting the tube to a pressurized gas tank; and a valve in or connected with the hose and configured to control gas flow from the pressurized gas tank through the hose.

[0118] 9. The drop probe system of clause 1, wherein the drop probe further comprises a transmitter in communication with the computing device and configured to transmit data from the drop probe to a remote computer.

[0119] 10. A method of using the drop probe system of clause 1, comprising implanting the drop probe into surface snow on a mountain; and transmitting data relating to properties of the surface snow.

[0120] 11. The method of clause 10, further comprising calculating the mass of the surface snow.

[0121] 12. The method of clause 10, wherein the drop probe is implanted by dropping the drop probe into the surface snow.

[0122] 13. The method of clause 12, wherein the drop probe is dropped by a drone into the surface snow. 14- A computer system for calculating the water content of surface snow on a mountain, the system comprising: a processor; computer memory storage accessible to the processor, and computer program instructions encoded in the computer memory storage, wherein, when the computer program instructions are processed by the processing system, the computer system is configured to: define data structures in the computer memory storage representing data from the drop probe system of clause 1; and execute algorithms of Equations (2) to (19) applied to the data structures to calculate the water content of surface snow in which the drop probe is dropped on a mountain.

[0123] 15. A computer program product comprising computer memory storage and computer program instructions encoded in the computer memory storage, wherein the computer program instructions, when processed by a processor of a computer, causes the computer to determine the mass of the surface snow from the method of clause 10.

[0124] While this invention has been shown and described with references to particular implementations thereof, those skilled in the art will understand that various substitutions and alterations in form and details may be made therein without departing from the scope of the invention. Further, other aspects, functions, and advantages are also within the scope of the invention, and all implementations of the invention need not necessarily achieve all of the advantages or possess all of the characteristics described above. Additionally, steps, elements, and features discussed herein in connection with one implementation can likewise be used in conjunction with other implementations. The contents of references, including reference texts, journal articles, patents, patent applications, etc., cited throughout the text are hereby incorporated by reference in their entirety for all purposes; and all appropriate combinations of implementations, features, characterizations, and methods from these references and the present disclosure may be included in implementations of this invention. Further still, the components and steps identified in the Background section are integral to this disclosure and can be used in conjunction with or substituted for components and steps described elsewhere in the disclosure within the scope of the invention.

Claims

CLAIMSWhat is claimed is:

1. A drop probe system including a drop probe including a nose at one end and a tail at an opposite end of an elongated body, the drop probe comprising: a power source contained in the elongated body; a computing device including a processor and a timing device and in electrical communication with the power source; an on-board accelerometer in communication with the computing device; a global positioning system in communication with the computing device; a motion sensor in communication with the computing device; a thermocouple in communication with the computing device; a weighted mass positioned proximate to the nose to place a center of gravity of the drop probe closer to the nose than a center of pressure of the drop probe, as measured when the drop probe orthogonally penetrates a bed of snow with the nose leading; and an attachment mechanism at the tail for attachment to cordage.

2. The drop probe system of claim 1, wherein the drop probe is less than about 30 cm long from nose to tail and has a mass of less than about 2 kg.

3. The drop probe system of claim 1, wherein the motion sensor is an optical motion sensor.

4. The drop probe system of claim 1, wherein the attachment mechanism is a hook.

5. The drop probe system of claim 1, further comprising a display screen in communication with the computing device and configured to display data based on measurements from at least one of the accelerometer, the global positioning system, the motion sensor, or the thermocouple.

6. The drop probe system of claim 1, further comprising an unmanned aerial vehicle (UAV), wherein the drop probe is attached to the UAV by a motorized winch comprising a brake and release mechanism.

7. The drop probe system of claim 1, further comprising a spool configured for hand dropping the drop probe, wherein the drop probe is configured for entry into snow on a slope.

8. The drop probe system of claim 1, further comprising a cannon configured for propelling the drop probe more than 10 meters, wherein the cannon comprises: a tube with packing material at its base; a hose connecting the tube to a pressurized gas tank; and a valve in or connected with the hose and configured to control gas flow from the pressurized gas tank through the hose.

9. The drop probe system of claim 1, wherein the drop probe further comprises a transmitter in communication with the computing device and configured to transmit data from the drop probe to a remote computer.

10. A method of using the drop probe system of claim 1, comprising implanting the drop probe into surface snow on a mountain; and transmitting data relating to properties of the surface snow.

11. The method of claim 10, further comprising calculating the mass of the surface snow.

12. The method of claim 10, wherein the drop probe is implanted by dropping the drop probe into the surface snow.

13. The method of claim 12, wherein the drop probe is dropped by a drone into the surface snow.

14. A computer system for calculating the water content of surface snow on a mountain, the system comprising: a processor; computer memory storage accessible to the processor, and computer program instructions encoded in the computer memory storage, wherein, when the computer program instructions are processed by the processing system, the computer system is configured to: define data structures in the computer memory storage representing data from the drop probe system of claim 1; and execute algorithms of Equations (2) to (19) applied to the data structures to calculate the water content of surface snow in which the drop probe is dropped on a mountain.

15. A computer program product comprising computer memory storage and computer program instructions encoded in the computer memory storage,wherein the computer program instructions, when processed by a processor of a computer, causes the computer to determine the mass of the surface snow from the method of claim 10.

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